$1,100 per month for 10 years, if the account earns 2% per year What the student or parent is asking is: If they deposit $1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly. 1100 per month. * 12 months in a year = 13,200 per year in deposit Since we matched interest crediting period with deposits, we now want to know: If they deposit $13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? This is an annuity, which is a constant stream of payments with interest crediting at a certain period. [SIZE=5][B]Calculate AV given i = 0.02, n = 10[/B] [B]AV = Payment * ((1 + i)^n - 1)/i[/B][/SIZE] [B]AV =[/B]13200 * ((1 + 0.02)^10 - 1)/0.02 [B]AV =[/B]13200 * (1.02^10 - 1)/0.02 [B]AV =[/B]13200 * (1.2189944199948 - 1)/0.02 [B]AV =[/B]13200 * 0.21899441999476/0.02 [B]AV = [/B]2890.7263439308/0.02 [B]AV = 144,536.32[/B]

$100 is invested in a bank account that gives an annual interest rate of 3%, compounded monthly. How much money will be in the account after 7 years? 7 years * 12 months per year = 84 periods. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=100&nval=84&int=3&pl=Monthly']compound interest calculator[/URL], we get an account balance of: [B]123.34[/B]

$1000 is invested with interest at a rate of 15% per year for 9 years. Find the amount you would have, if it’s continuously compounded Using [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=15&t=9&pl=Continuous+Interest']our balance calculator[/URL], we get: [B]$3,857.43[/B]

$13,000 is compounded semiannually at a rate of 11% for 20 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=13000&nval=40&int=11&pl=Semi-Annually']compound interest calculator with t = 20 years * 2 semi-annual periods per year = 40[/URL], we get: [B]110,673.01[/B]

$2,030.00 was invested at 10% per annum compounded annually. What interest has been earned (in dollars correct to the nearest cent) after 5 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=2030&nval=5&int=10&pl=Annually']compound interest calculator[/URL], we get: [B]3,269.34[/B]

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years So we have: [LIST] [*]$300 principal [*]13 * 2 = 26 periods for n [*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period [/LIST] Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get: [B]$831.74[/B]

$4700 at 3.5% for 6 years compounded monthly 6 years = 12*6 = 72 months or compounding periods. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=4700&nval=72&int=3.5&pl=Monthly']balance with interest calculator[/URL], we get a final balance of: [B]$5,796.51[/B]

$500 is deposited into a savings account. The bank offers a 3.5% interest rate and the money is left in the account for 5 years. How much interest is earned in this situation? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=5000&nval=5&int=3.5&pl=Annually']compound interest calculator[/URL], we get interest earned as: [B]938.43[/B]

$800 is deposited in an account that pays 9% annual interest find balance after 4 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=800&nval=4&int=9&pl=Annually']compound interest calculator[/URL], we get: [B]1,129.27[/B]

$8000 are invested in a bank account at an interest rate of 10 percent per year. Find the amount in the bank after 5 years if interest is compounded annually Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=8000&nval=5&int=10&pl=Annually']compound interest with balance calculator[/URL], we get: [B]12,884.08[/B]

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How old is John right now? If Mike will be 40 1 year from now, then he is: 40 - 1 = 39 years old today. And if the current sum of Mike and John's age is 89, then we use j for John's age: j + 39 = 89 [URL='https://www.mathcelebrity.com/1unk.php?num=j%2B39%3D89&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]j = 50[/B]

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How old is Sharon right now? If Paul will be 49 years old 1 year from now, this means today, he is 49 - 1 = 48 years old. Let Sharon's age be s. Then from the current sum of Paul and Sharon's ages, we get: s + 49 = 85 [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B49%3D85&pl=Solve']Type this equation into our search engine[/URL], and get: s = [B]36[/B]

2200 dollars is placed in an account with an annual interest rate of 7.25%. How much will be in the account after 29 years [URL='https://www.mathcelebrity.com/compoundint.php?bal=2200&nval=29&int=7.25&pl=Annually']Using our compound interest calculator[/URL], with an initial balance of 2,200, 29 years for time, and 7.25% annual interest rate, we get: [B]16,747.28[/B]

2900 dollars is placed in an account with an annual interest rate of 9%. Hoe much will be in the account after 13 years to the nearest cent Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2900&nval=13&int=9&pl=Annually']compound interest with balance calculator[/URL], we get: [B]8,890.83[/B]

2900 dollars is placed in an account with annual interest rate of 9%. How much will be in the account after 13 years, round to the nearest cent Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2090&nval=13&int=9&pl=Annually']compound interest calculato[/URL]r, we get a balance of: [B]6,407.53[/B]

Free 401(k) Balance Calculator - Determines your 401(k) balance given a salary history per year, contribution percentage rate, employer match percentage, and a rate of return.

4K a month how much in a year 4K = 4000, so we have: 4000 per month * 12 months / year = [B]48,000 per year[/B]

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now? Let Kevin's age be k. Let Tami's age be t. We're given the following equations: [LIST=1] [*]k - 5 = 3(t - 5) [*]k = 2t [/LIST] Plug equation (2) into equation (1) for k: 2t - 5 = 3(t - 5) We p[URL='https://www.mathcelebrity.com/1unk.php?num=2t-5%3D3%28t-5%29&pl=Solve']lug this equation into our search engine[/URL] and we get: t = [B]10. Tami's age[/B] Now plug t = 10 into equation (2) to solve for k: k = 2(10) k =[B] 20. Kevin's age[/B]

6 boys have a mean age of 10 years and 14 girls have a mean age of 5 work out the mean age of the 20 children [U]Calculate Sum of boys ages:[/U] Sum of boys ages/6 = 10 Cross multiply, and we get: Sum of boys ages = 6 * 10 Sum of boys ages = 60 [U]Calculate Sum of girls ages:[/U] Sum of girls ages/14 = 5 Cross multiply, and we get: Sum of girls ages = 14 * 5 Sum of girls ages = 70 Average of 20 children is: Average of 20 children = (Sum of boys ages + sum of girls ages)/20 Average of 20 children = (60 + 70)/20 Average of 20 children = 130/20 Average of 20 children = [B]6.5 years[/B]

6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will be 91. how old is Jose right now? Let c be Cindy's age and j be Jose's age. We have: c + 6 = 25 This means c = 19 using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B6%3D25&pl=Solve']equation calculator[/URL]. We're told in 12 years, c + j = 91. If Cindy's age (c) is 19 right now, then in 12 years, she'll be 19 + 12 = 31. So we have 31 + j = 91. Using our [URL='https://www.mathcelebrity.com/1unk.php?num=31%2Bj%3D91&pl=Solve']equation calculator[/URL], we get [B]j = 60[/B].

6700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 24 years, to the nearest cent? [URL='https://www.mathcelebrity.com/intbal.php?startbal=6700&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2024&pl=Annual+Credit']Using our balance with interest calculator[/URL], we get: [B]$42,485.94[/B]

6700 dollars is placed in an account with an annual interest rate of 8%. show much will be in the account after 24 years, to the nearest cent ? Using our compound interest calculator, we get: [B]42,485.91 [MEDIA=youtube]0C25FB_4004[/MEDIA][/B]

6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6700&nval=28&int=8.25&pl=Annually']balance with interest calculator[/URL], we get: 61,667.47

7100 dollars is placed in an account with an annual interest rate of 7.75%. How much will be in the account after 30 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with compound interest calculator[/URL], we get: 66,646.40

7100 dollars is placed in an account with an interest of 7.75%. How much will be in the account after 30 years to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with interest calculator[/URL], we get: [B]$66,646.40[/B]

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the account after 24 years, to the nearest cent? [URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=24&int=5.75&pl=Annually']Using our balance with interest calculator[/URL], we get: [B]$29,459.12[/B]

7900 dollars is placed in an account with an annual interest rate of 5.5%. How much will be in the account after 11 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7900&nval=11&int=5.5&pl=Annually']compound interest calculator[/URL], we get: [B]14,236.53[/B]

8 years from now a girls age will be 5 times her present age whats is the girls age now. Let the girl's age now be a. We're given: a + 8 = 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D5a&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 2[/B]

8300 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 14 years, to the nearest cent? [URL='https://www.mathcelebrity.com/compoundint.php?bal=8300&nval=14&int=6.5&pl=Annually']Using our balance with interest calculator[/URL], we get: [B]$20,043.46[/B]

9000 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 17 years, to the nearest cent? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=9000&nval=17&int=8&pl=Annually']compound interest accumulated balance calculator[/URL], we get: [B]$33,300.16[/B]

A $1,000 deposit is made at a bank that pays 12% compounded monthly. How much will you have in your account at the end of 10 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=10000&nval=120&int=12&pl=Monthly']compound interest calculator[/URL] with time = 10 years * 12 months per year = 120, we get: [B]33,003.87[/B]

A $1,000 investment takes a 10% loss each year. What will be the value 3 years? 10% is 0.1. Our Balance function B(y) where y is the number of years since the start is: B(y) = 1000(1 - 0.1)^y B(y) = 1000(0.9)^y We want to know B(3): B(3) = 1000(0.9)^3 B(3) = 1000(0.729) B(3) = [B]729[/B]

A 1975 comic book has appreciated 8% per year and originally sold for $0.26. What will the comic book be worth in 2020 Calculate the number of years: 2020 - 1975 = 45 Set up the accumulation function A(t) where t is the number of years since 1975: A(t) = 0.26(1.08)^t We want A(45) A(45) = 0.26(1.08)^45 A(45) = 0.26 * 32.9045 A(45) = [B]8.30[/B]

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010. Find the number of muffins sold after 2010 through 2015: 7,420 - 5,800 = 1,620 Now, since the problem states a linear sales model, we need to determine the sales per year: 1,620 muffins sold since 2010 / 5 years = 324 muffins per year. Build our linear model: [B]y = 5,800 + 324x [/B] Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970 The formula for accumulated value of something with a percentage growth p and years x is: V(x) = Initial Value * (1 + p/100)^x Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have: V(x) = 100 * (1 + 8/100)^50 V(x) = 100 * (1.08)^50 V(x) = 100 * 46.9016125132 V(x) = [B]4690.16[/B]

A basket of goods was valued at $45.40 in January 2011. The inflation rate for the year was 4%. What is the expected cost of the basket of goods in January 2012? Write your answer to the nearest cent. 2012 cost = 2011 cost * (1 + I/100) 2012 cost = 45.40 * (1 + 4/100) 2012 cost = 45.40 * (1 + 0.04) 2012 cost = 45.40 * (1.04) 2012 cost = [B]47.22[/B]

A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that represents the length y (in feet) of a boa constrictor that is x years old. 8 inches per year = 8/12 feet = 2/3 foot [B]y = 18 + 2/3x[/B]

A boat costs 14950 and decrease in value by 7% per year how much will the boat be worth after 8 years? If a boat decreases in value 7% in value, then our new value each year is 100% - 7% = 93%. So we have a B(y) function where B(y) is the value of the boat after y years: B(y) = 14,950 * (1 - 0.07)^y Simplifying, we get: B(y) = 14,950 * (0.93)^y The problem asks for B(8) B(8) = 14,950 * (0.93)^7 B(8) = 14,950 * 0..6017 B(8) = [B]8,995.43[/B]

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each? Let the boy's age be b and his brother's age be c. We're given two equations: [LIST=1] [*]b = c + 10 [*]b + 4 = 2(c + 4) [/LIST] Substitute equation (1) into equation (2): (c + 10) + 4 = 2(c + 4) Simplify by multiplying the right side through and grouping like terms: c + 14 = 2c + 8 [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B14%3D2c%2B8&pl=Solve']Type this equation into our search engine[/URL] and we get: c = [B]6[/B] Now plug c = 6 into equation (1): b = 6 + 10 b = [B]16[/B]

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages? Let b be the boy's age and s be his sister's age. We're given two equations: [LIST=1] [*]b = s + 6 [*]b + 3 = 2(s + 3) [/LIST] Plug in (1) to (2): (s + 6) + 3 = 2(s + 3) s + 9 = 2s + 6 [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B9%3D2s%2B6&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]s = 3[/B] We plug s = 3 into Equation (1) to get the boy's age (b): b = 3 + 6 [B]b = 9[/B]

A boy is 6 years younger than his sister. If he is (x-9) years old, how long will it take for his sister to be x years old? If the boy is x - 9 years old, and he's 6 years younger than his sister, than the sister is older by 6 years. Sister's Age = x - 9 + 6 Sister's Age = x - 3 In order to be x years old, we must add 3 years: x - 3 + 3 = x So in [B]3 years, [/B]the sister will be x years old.

A brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value of the car after 6 years? The Book Value depreciates 8% per year. We set up a depreciation equation: BV(t) = BV(0) * (1 - 0.08)^t The Book Value at time 0 BV(0) = 25,000. We want the book value at time 6. BV(6) = 25,000 * (1 - 0.08)^6 BV(6) = 25,000 * 0.92^6 BV(6) = 25,000 * 0.606355 BV(6) = [B]15,158.88[/B]

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be in 10 years? Find the number of doubling periods: Number of Doubling periods = Time / Doubling period Number of Doubling periods = 10/2 Number of Doubling periods = 5 Create a function to determine the amount of bunnies after each doubling period: B(n) = 45 * 2^n Since we calculated 5 doubling periods, we want B(5): B(5) = 45 * 2^5 B(5) = 45 * 32 B(5) = [B]1,440[/B]

A car is bought for $2400 and sold one year later $1440 find the loss as a percentage of the cost price. (2400 - 1440)/2400 960/2400 0.4 As a percentage, we multiply by 100 to get [B]40%[/B]

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. Set up the depreciation equation D(t) where t is the number of years in the life of the car: D(t) = 24,000 * (1 - 0.3)^t D(t) = 24000 * (0.7)^t The problem asks for D(t)<=7300 24000 * (0.7)^t = 7300 Divide each side by 24000 (0.7)^t = 7300/24000 (0.7)^t= 0.30416666666 Take the natural log of both sides: LN(0.7^t) = -1.190179482215518 Using the natural log identities, we have: t * LN(0.7) = -1.190179482215518 t * -0.35667494393873245= -1.190179482215518 Divide each side by -0.35667494393873245 t = 3.33687437943 [B]Rounding this up, we have t = 4[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years? Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t: B(t) = 19,000(1-0.3)^t Simplifying this, we get: B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I] The problem asks for B(4): B(4) = 19,000(0.7)^4 B(4) = 19,000(0.2401) B(4) = [B]4,561.90[/B]

A car is purchased for 27,000$. After each year the resale value decreases by 20%. What will the resale value be after 3 years? If it decreases by 20%, it holds 100% - 20% = 80% of the value each year. So we have an equation R(t) where t is the time after purchase: R(t) = 27,000 * (0.8)^t The problem asks for R(3): R(3) = 27,000 * (0.8)^3 R(3) = 27,000 * 0.512 R(3) = [B]13.824[/B]

a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000 Let y be the number of years. We want to know y when: 24000 - 3000y = 9000 Typing [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000y%3D9000&pl=Solve']this equation into our search engine[/URL], we get: y = [B]5[/B]

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that describes the relationship between the value of the car (C) and the time after it has been purchased (t)? Let t be the number of years since purchase. Depreciation means the value decreases, so we have: [B]C = 43000 - 2000t[/B]

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters of the value at the beginning of the year. Write the first four terms of the sequence of the car’s value at the end of each year. three-quarters means 3/4 or 0.75. So we have the following function P(y) where y is the number of years since purchase price: P(y) = 24000 * 0.75^y First four terms: P(1) = 24000 * 0.75 = [B]18000[/B] P(2) = 18000 * 0.75 = [B]13500[/B] P(3) = 13500 * 0.75 = [B]10125[/B] P(4) = 10125 * 0.75 = [B]7593.75[/B]

A celebrity 50,000 followers on Instagram. The number of follower increases 45% each year. How many followers will they have after 8 years? We set up a growth equation for followers F(y), where y is the number of years passed since now: F(y) = 50000 * (1.45)^y <-- since 45% is 0.45 The problem asks for F(8): F(8) = 50000 * 1.45^8 F(8) = 50000 * 19.5408755063 F(8) = [B]977,044[/B]

A certain textbook cost $94. If the price increases each year by 3% of the previous year's price, find the price after 7 years. Using our [URL='https://www.mathcelebrity.com/apprec-percent.php?num=acertaintextbookcost94.ifthepriceincreaseseachyearby3%ofthepreviousyearspricefindthepriceafter7years&pl=Calculate']appreciation calculator[/URL], we get: [B]115.61[/B]

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hidden BC stands for Before Christ. Year 0 is when Christ was born. AD stands for After Death On a number line, the point of Christ's birth is 0. So BC is really negative AD is positive So we have: 284 - -64 284 + 64 [B]348 years[/B]

A city doubles its size every 48 years. If the population is currently 400,000, what will the population be in 144 years? Calculate the doubling time periods: Doubling Time Periods = Total Time / Doubling Time Doubling Time Periods = 144/48 Doubling Time Periods = 3 Calculate the city population where t is the doubling time periods: City Population = Initital Population * 2^t Plugging in our numbers, we get: City Population = 400,000 * 2^3 City Population = 400,000 * 8 City Population = [B]3,200,000[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 9 years? Let's build a population function P(t), where t is the number of years since right now. P(t) = 240,000(1.0725)^t <-- 7.25% as a decimal is 0.0725 The question asks for P(9) P(9) = 240,000(1.0725)^9 P(9) = 240,000(1.87748) P(9) = [B]450,596[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What will the population be after 5 years? [U]Set up our population function[/U] P(t) = 240,000(1 + t)^n where t is population growth rate percent and n is the time in years [U]Evaluate at t = 0.08 and n = 5[/U] P(5) = 240,000(1 + 0.08)^5 P(5) = 240,000(1.08)^5 P(5) = 240,000 * 1.4693280768 [B]P(5) = 352638.73 ~ 352,639[/B]

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . What will the population be after 12 years? Use the calculator provided and round your answer to the nearest whole number. Using our [URL='http://www.mathcelebrity.com/population-growth-calculator.php?num=acityhasapopulationof260000people.supposethateachyearthepopulationgrowsby8.75%.whatwillthepopulationbeafter12years?usethecalculatorprovidedandroundyouranswertothenearestwholenumber&pl=Calculate']population growth calculator,[/URL] we get P = [B]711,417[/B]

A college student earned $6000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 6%. If the student received a total of $418 in interest at the end of the year, how much was invested at 8%? [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=6&itot=418&pl=Calculate']Using our split fund interest calculator[/URL], we get: [B]$2,900 invested at 8%[/B] $3,100 invested at 6%

A comet passes earth every 70 years. another comet passes earth every 75 years of both comets pass earth this year how many years will it be before they pass on the same year again. We want the least common multiple of (70, 75). [URL='https://www.mathcelebrity.com/gcflcm.php?num1=70&num2=75&num3=&pl=GCF+and+LCM']Using our LCM calculator[/URL], we find the answer is [B]1,050 years[/B]

A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years. What is the probability that a CD will last less than 3 years? Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=3&mean=4&stdev=0.8&n=1&pl=P%28X+%3C+Z%29']Z-score and Normal distribution calculator[/URL], we get: [B]0.10565[/B]

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number. We build the following exponential equation: Final Balance = Initial Balance * (1 + growth rate)^time Final Balance = 3100(1.04)^6 Final Balance = 3100 * 1.2653190185 Final Balance = 3922.48895734 The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U] Final Balance = [B]3,922[/B]

a company made a profit of $4 million per month for 8 months, then lost $10 million per month for 4 months. What was their result for the year? Profits = 4 million per month * 8 months = 32,000,000 Losses = 10 million per month * 4 months = 40,000,000 Calculate results for the year: Result for the year = Profits - Losses Result for the year = 32,000,000 - 40,000,000 Result for the year = [B]8,000,000[/B]

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per year through retirements, until its total employment is 2560. How long will this take? Figure out how many reductions are needed 4900 - 2560 = 2340 We want 300 per year for retirements, so let x equal how many years we need to get 2340 reductions. 300x = 2340 Divide each side by 300 x = 7.8 years. If we want full years, we would do 8 full years

a computer is purchased for 800 and each year the resale value decreases by 25% what will be the resale value after 4 years Let the resale in year y be R(y). We have: R(y) = 800 * (1 - 0.25)^y R(y) = 800 * (0.75)^y The problem asks for R(4): R(4) = 800 * (0.75)^4 R(4) = 800 * 0.31640625 R(4) = [B]$253.13[/B]

A couple is opening a savings account for a newborn baby. They start with $3450 received in baby gifts. If no depositts or withdrawals are made, what is the balance of the account if it earns simple interest at 6% for 18 years? Using [URL='https://www.mathcelebrity.com/simpint.php?av=&p=3450&int=6&t=18&pl=Simple+Interest']our simple interest calculator[/URL], we get: [B]7,176[/B]

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate. [U]Calculate Monthly Nominal Rate:[/U] Monthly Nominal Rate = Annual Rate / 12 months per year Monthly Nominal Rate = 36%/12 Monthly Nominal Rate = 3% [U]Since there are 12 months in a year, we compound 12 times to get the effective rate below:[/U] Effective Rate = (1 + Monthly Nominal Rate as a Decimal)^12 - 1 Since 3% = 0.03, we have: Effective Rate = 100% * ((1 + 0.03)^12 - 1) Effective Rate = 100% * ((1.03)^12 - 1) Effective Rate = 100% * (1.42576088685 - 1) Effective Rate = 100% * (0.42576088685) Effective Rate = [B]42.58%[/B]

A father is K years old and his son is M years younger. The sum of their ages is 53. Father's Age = K Son's Age = K - M and we know K + (K - M) = 53 Combine like terms: 2K - M = 53 Add M to each side: 2K - M + M = 53 + M Cancel the M's on the left side, we get: 2K = 53+ M Divide each side by 2: 2K/2 = (53 + M)/2 Cancel the 2's on the left side: K = [B](53 + M)/2[/B]

A football team gained 4 yards on a play,lost 8 on the next play ,then gained 2 yards on the third play write and addition expression Gains are expressed with positives (+) and losses are expressed with negatives (-): [LIST] [*]Gained 4 years: +4 [*]Lost 8 on the next play: -8 [*]Gained 2 yards on the third play: +2 [/LIST] Expression: [B]+4 - 8 + 2 = -2[/B]

A fuel injection system is designed to last 18 years, with a standard deviation of 1.4 years. What is the probability that a fuel injection system will last less than 15 years? Using our [URL='https://www.mathcelebrity.com/probnormdist.php?xone=15&mean=18&stdev=14&n=1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that: P(X < 15) = [B]0.416834[/B]

A giant tortoise can live 175 years in captivity. The gastrotrich, which is a small aquatic animal, has a life-span of only 3 days (72 hours). If a gastrotrich died after 36 hours, a giant tortoise that lived 87.5 yeas would live proportionally the same because they both would have died halfway through their life-span. How long would a giant tortoise live if it lived proportionally the same as a gastrotrich that died after 50 hours? Set up a proportion of hours lived to lifespan where n is the number of years the giant tortoise lives: 50/72 = n/175 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=50&num2=n&den1=72&den2=175&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: n = [B]121.5[/B]

A girl is three years older than her brother. If their combined age is 35 years, how old is each Let the girl's age be g. Let the boy's age be b. We're given two equations: [LIST=1] [*]g = b + 3 ([I]Older means we add)[/I] [*]b + g = 35 [/LIST] Now plug in equation (1) into equation (2) for g: b + b + 3 = 35 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb%2B3%3D35&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]16 [/B] Now, to solve for g, we plug in b = 16 that we just solved for into equation (1): g = 16 + 3 g = [B]19[/B]

A grandmother deposited $5,000 in an account that pays 8% per year compounded annually when her granddaughter was born. What will the value of the account be when the granddaughter reaches her 16th birthday? We have the accumulation function A(t) = 5,000(1.08)^t. For t = 16, we have: A(16) = 5,000(1.08)^16 A(16) = 5,000*3.42594264333 A(16) = [B]17,129.71[/B]

A group of people were asked if they had run a red light in the last year. 497 responded "yes", and 223 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year. P(Run Red Light) = yes answers / total answers P(Run Red Light) = 497 / (497 + 223) P(Run Red Light) = 497 / 720 P(Run Red Light) = [B]0.6903[/B]

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989. Let's determine the years: 2000 - 1989 = 11 Let's determine the change in value: 125,000 - 70,000 = 55,000 Assuming a linear progression, we have: 55,000/11 = 5,000 per year increase [B]y = 70,000 + 5,000v[/B] where v is the number of years after 1989 Plug in 11 to check our work y = 70,000 + 5,000(11) y = 70,000 + 55,000 y = 125,000

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. What is the probability of selecting a participant who is at least 20 years old? At least 20 means 20 or older, so our selection of individuals is: {20, 26, 27, 28, 30} This is 5 out of a possible 8, so we have [URL='http://www.mathcelebrity.com/perc.php?num=5&den=8&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']5/8 of 0.625, which is 62.5%[/URL]

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b We're given 3 equations: [LIST=1] [*]a = b + 2 [*]b = 2c [*]a + b + c = 42 [/LIST] Substituting equation (2) into equation (1), we have: a = 2c + 2 Since b = 2c, we substitute both of these into equation (3) to get: 2c + 2 + 2c + c = 42 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B2%2B2c%2Bc%3D42&pl=Solve']type this equation into our math engine[/URL] and we get: c = 8 Now take c = 8 and substitute it into equation (2) above: b = 2(8) b = [B]16[/B]

A laptop is purchased for $1700. After each year, the resale value decreases by 25%. What will be the resale value after 5 years? [U]Let R(t) be the Resale value at time t:[/U] R(t) = 1,700(1 - 0.25)^t [U]We want R(5)[/U] R(5) = 1,700(1 - 0.25)^5 R(5) =1,700(0.75)^5 R(5) =1,700 * 0.2373 R(5) = [B]$403.42[/B]

A local college classifies its students by major, year (Freshman, Sophomore, Junior, Senior) and sex (M, F). If the college offers 20 majors, how many combinations are possible? We have 20 majors, 4 grade levels, and 2 sexes. The total combinations = 20 * 4 * 2 = [B]160[/B]

A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year’s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago? Declare variable and convert numbers: [LIST] [*]16% = 0.16 [*]let the sales 2 years ago be s. [/LIST] s(1 + 0.16)(1 + 0.16) = 80,642 s(1.16)(1.16) = 80,642 1.3456s = 80642 Solve for [I]s[/I] in the equation 1.3456s = 80642 [SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE] 1.3456s/1.3456 = 80642/1.3456 s = 59930.142687277 s = [B]59,930.14[/B]

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit is only $5.50. What is the least number of visits needed in a year in order for the membership to be a better deal? Set up the cost for the visitors plan C(v) where v is the number of visits: C(v) = 8v Set up the cost for the membership plan C(v) where v is the number of visits: C(v) = 5v + 45 The problem asks for v where: 5v + 45 < 8v [URL='https://www.mathcelebrity.com/1unk.php?num=5v%2B45%3C8v&pl=Solve']Type this inequality into our search engine[/URL] and get: v > 15 This means, the least number of visits is 1 more which is [B]16[/B]

a machine has a first cost of 13000 an estimated life of 15 years and an estimated salvage value of 1000.what is the book value at the end of 9 years? Using [URL='https://www.mathcelebrity.com/depsl.php?d=&a=13000&s=1000&n=15&t=9&bv=&pl=Calculate']our straight line depreciation calculator[/URL], we get a book value at time 9, B9 of: [B]5,800[/B]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: [LIST=1] [*]m = w + 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Rearrange equation 1 in terms of w my subtracting 5 from each side: [LIST=1] [*]w = m - 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Substitute equation (1) and equation (2) into equation (3) 0.5m + m + m - 5 = 100 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]42 [/B] Now, substitute m = 42 into equation 2 to solve for d: d = 0.5(42) d = [B]21 [/B] Now substitute m = 42 into equation 1 to solve for w: w = 42 - 5 w = [B]37 [/B] To summarize our ages: [LIST] [*]Man (m) = 42 years old [*]Daughter (d) = 21 years old [*]Wife (w) = 37 years old [/LIST]

A man is four times as old as his son. In five years time he will be three times as old. Find their present ages. Let the man's age be m, and the son's age be s. We have: [LIST=1] [*]m = 4s [*]m + 5 = 3(s + 5) [/LIST] Substitute (1) into (2) 4s + 5 = 3s + 15 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D3s%2B15&pl=Solve']equation calculator[/URL], and we get [B]s = 10[/B]. m = 4(10) [B]m = 40[/B]

A man's age (a) 10 years ago is 43 [U]10 years ago means we subtract 10 from a:[/U] a - 10 [U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U] [B]a - 10 = 43[/B] If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get: a = 53

A man's age (a) 10 years ago is 43. Years ago means we subtract [B]a - 10 = 43 [/B] If the problem asks you to solve for a, we type this equation into our math engine and we get: Solve for [I]a[/I] in the equation a - 10 = 43 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 43. To do that, we add 10 to both sides a - 10 + 10 = 43 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] a = [B]53[/B]

a mans age (a) ten years ago The problem asks for an algebraic expression for age. The phrase [I]ago[/I] means before now, so they were younger. And younger means we [B]subtract[/B] from our current age: [B]a - 10[/B]

A man’s age 10 years ago, if he is now n years old. 10 years ago means we subtract from current age: [B]n - 10[/B]

A milk booth sells 445 litres of milk in a day. How many litres of milk will it sell in 4 years Calculate the number of days in 4 years: Days in 4 years = Days in 1 year * 4 Days in 4 years = 365 * 4 Days in 4 years = 1,460 Calculate litres of milk sold in 4 years: Litres of milk sold in 4 years = Litres of milk sold in 1 day * Days in 4 years Litres of milk sold in 4 years = 445 * 1,460 Litres of milk sold in 4 years = [B]649,700 litres[/B]

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars value will be $9,000 We have a flat rate depreciation each year. Set up the function D(t) where t is the number of years of depreciation: D(t) = 24000 - 3000t The problem asks for the time (t) when D(t) = 9000. So we set D(t) = 9000 24000 - 3000 t = 9000 To solve for t, [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000t%3D9000&pl=Solve']we plug this function into our search engine[/URL] and we get: t = [B]5[/B]

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000 Step 1, the question asks for Book Value. Let y be the number of years since purchase. We setup an equation B(y) which is the Book Value at time y. B(y) = Sale Price - Depreciation Amount * y We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000 30000 - 3000y = 9000 To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get: y = [B]7 [/B] To check our work, substitute y = 7 into B(y) B(7) = 30000 - 3000(7) B(7) = 30000 - 21000 B(7) = 9000 [MEDIA=youtube]oCpBBS7fRYs[/MEDIA]

a new savings account starts at $700 at a rate of 1.2% yearly. how much money will be in the account after 8 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=1.2&pl=Annually']balance and interest calculator with annual (yearly) compounding[/URL], we have: [B]770.09[/B]

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this investment be worth in 10 years? If the interest was applied four times per year (known as quarterly compounding), calculate how much the investment would be worth after 10 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=10&int=4&pl=Annually']compound interest calculator[/URL], $500 @ 4% for 10 years is: $[B]740.12 [/B] Using [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=40&int=4&pl=Quarterly']quarterly compounding in our compound interest calculator[/URL], we have 10 years * 4 quarters per year = 40 periods, so we have: [B]$744.43[/B]

A person invests $9400 in an account at 5% interest compound annually. When will the value of the investment be $12,800. Let's take it one year at a time: Year 1: 9,400(1.05) = 9,870 Year 2: 9,870(1.05) = 10,363.50 Year 3: 10,363.50(1.05) = 10,881.68 Year 4: 10.881.68(1.05) = 11,425.76 Year 5: 11,425.76(1.05) = 11,997.05 Year 6: 11,997.05(1.05) = 12.596.90 Year 7: 12,596.90(1.05) = 13,226.74 So it take [B][U]7 years[/U][/B] to cross the $12,800 amount.

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get: V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years. Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get: V = 96,300 * e^(0.028 * 7) V = 96,300 * e^0.196 V = 96,300 * 1.21652690533 V = [B]$117,151.54[/B]

A person will devote 31 years to be sleeping and watching tv. The number of years sleeping will exceed the number of years watching tv by 19. How many years will the person spend on each of these activities Let s be sleeping years and t be tv years, we have two equations: [LIST=1] [*]s + t = 31 [*]s = t + 19 [/LIST] Substitute (2) into (1) (t + 19) + t = 31 Combine like terms: 2t + 19 = 31 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2t%2B19%3D31&pl=Solve']equation solver[/URL], we get [B]t = 6[/B]. Using equation (2), we have s = 6 + 19 s = [B]25[/B]

A piece of gym equipment which cost 450 including vat last year is now selling at 500 excluding vat. Calculate the percentage increase. Increase = (New Price - Old Price)/Old Price Increase = (500-450)/450 50/450 = 0.1111 To get the percentage, multiply by 100 [B]11.11%[/B]

A plumber makes a starting $36,000 a year. They get paid semimonthly. They have a health insurance premium of $74.28 and $25 in union dues each paycheck. 1. What is their semimonthly salary? Calculate the number of semi-monthly periods per year: Semi-monthly periods per year = 12 Months per year * 2 Semi-monthly periods per year = 24 Calculate semi-monthly salary amount: Semi-monthly salary amount = Annual Salary / Semi-monthly periods per year Semi-monthly salary amount = $36,000 / 24 Semi-monthly salary amount = $1,500 Now, calculate the net pay each semimonthly period: Net pay = Semi-monthly salary amount - Health Insurance Premium - Union Dues Net pay = $1,500 - $74.28 - $25 Net pay = [B]$1,400.72[/B]

A population grows at 6% per year. How many years does it take to triple in size? With a starting population of P, and triple in size means 3 times the original, we want to know t for: P(1.06)^t = 3P Divide each side by P, and we have: 1.06^t = 3 Typing this equation into our search engine to solve for t, we get: t = [B]18.85 years[/B] Note: if you need an integer answer, we round up to 19 years

A population of wolves on an island starts at 5 if the population doubles every 10 years, what will be the population in 90 years? If the population doubles every 10 years, we have 90/10 = 9 doubling periods. Our population function P(t) is where t is the doubling period P(t) = 5(2^t) The problem asks for P(9): P(9) = 5(2^9) P(9) = 5(512) P(9) = [B]2,560[/B]

A principal of $2200 is invested at 6% interest, compounded annually.How much will investment be worth after 10 years? Use our [URL='http://www.mathcelebrity.com/compoundint.php?bal=2200&nval=10&int=6&pl=Annually']balance calculator,[/URL] we get: [B]$3,939.86[/B]

A principal of $3300 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 10 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=3300&nval=10&int=3.25&pl=Annually']Using our balance calculator with compound interest[/URL], we get: [B]$4,543.75[/B]

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year. What will tuition be in 10 years? Let the tuition be T(y) where y is the number of years from now. We've got: T(y) = 36400 * (1.1)^y The problem asks for T(10) T(10) = 36400 * (1.1)^10 T(10) = 36400 * 2.5937424601 T(10) = [B]94,412.23[/B]

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year. What will tuition be in 3 years? We have the following appreciation equation A(y) where y is the number of years: A(y) = Initial Balance * (1 + appreciation percentage)^ years Appreciation percentage of 7% is written as 0.07, so we have: A(3) = 52,200 * (1 + 0.07)^3 A(3) = 52,200 * (1.07)^3 A(3) = 52,200 * 1.225043 A(3) = [B]63,947.25[/B]

A project requires a $5000 investment. It pays out $1000 at year 1, $2000 at year 2, $3000 at year 3. The discount rate is 5%. Should you invest? Using our [URL='https://www.mathcelebrity.com/npv.php?matrix1=0%2C-5000%0D%0A1%2C1000%0D%0A2%2C2000%0D%0A3%2C3000&irr=5&pl=NPV']NPV calculator,[/URL] we get: NPV = 357.94. Because NPV > 0, we [B]should invest [MEDIA=youtube]jXvwCTDwQ1o[/MEDIA][/B]

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.29 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (u1 - u2) What is the interpretation of this confidence interval? A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours B. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours C. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours D. There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours 0.2021 < u1 - u2 < 1.6579 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=2.31&n2=40&xbar2=4.29&stdev2=1.58&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means confidence interval calculator[/URL] [B]Choice D There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours[/B]

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds? For simple interest, we have: Balance * interest rate = Interest payment 8000i = 584 Divide each side of the equation by 8000 to isolate i: 8000i/8000 = 584/8000 Cancelling the 8000's on the left side, we get: i = 0.073 Most times, interest rates are expressed as a percentage. Percentage interest = Decimal interest * 100% Percentage interest = 0.073 * 100% Multiplying by 100 is the same as moving the decimal point two places right: Percentage interest = [B]7.3%[/B]

A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500 Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7500&nval=8&int=15&pl=Annually']compound interest with balance calculator,[/URL] we get a balance of: [B]22,942.67[/B]

a school fee is 32000 per year what is fees of one month 32000 per year / 12 months per year = [B]2666.67 per month[/B]

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per square yard. How much will the chalkboard cost? Area of a chalkboard is denoted as : A = lw Given 1 yard width and 2 years length of the chalkboard, we have: A = 2(1) A = 2 square yards Therefore, total cost is: Total Cost = $27.31 * square yards Total Cost = $27.31(2) Total Cost = [B]$54.62[/B]

A software company, in 3 consecutive years, makes profits of -3 million dollars, 10 million dollars, and -2 million dollars. What was its profit over the 3 year period? Profit = -3,o00,000 + 10,000,000 - 2,000,000 Profit = [B]5,000,000[/B]

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years Simple interest formula if we start with 1 dollar and double to 2 dollars: 1(1 + i(20)) = 2 1 + 20i = 2 Subtract 1 from each side: 20i = 1 Divide each side by 20 i = 0.05 Now setup the same simple interest equation, but instead of 2, we use 3: 1(1 + 0.05(t)) = 3 1 + 0.05t = 3 Subtract 1 from each side: 0.05t = 2 Divide each side by 0.05 [B]t = 40 years[/B]

A survey was conducted that asked 1007 people how many books they had read in the past year. Results indicated that x overbarequals11.3 books and sequals16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval. x bar = 11.3 s = 16.6 n = 1007 [URL='https://www.mathcelebrity.com/normconf.php?n=1007&xbar=11.3&stdev=16.6&conf=90&rdig=4&pl=Not+Sure']We use our confidence interval calculator[/URL] and get [B]10.4395 < u < 12.1605[/B]. [B][I]We interpret this as: If we repeated experiments, the proportion of such intervals containing u would be 90%[/I][/B]

A teacher who makes $54000 per year $8400 in taxes, and $1200 in union does what fraction of the teacher’s income does she have left Calculate Net Income: Net income = Earnings - Taxes - Union Dues Net income = 54000 - 8400 - 1200 Net income = 44,400 Net Income Percent = 100% * Net Income / Earnings Net Income Percent = 100% * 44,400/54,000 Net Income Percent = 100% * 0.8222 Net Income Percent = [B]82.22%[/B]

A theatre sold 67 tickets to a show. 43 tickets were for children up to 12 years old. How many tickets were for people older than 12 67 tickets - 43 tickets for 12 and under = [B]24 tickets[/B] for people older than 12

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearly interest amounted to $315, how much was invested at each rate? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4300&i1=6+&i2=9&itot=315&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]Fund 1: 2,400[/B] [*][B]Fund 2: 1,900[/B] [/LIST]

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number? We calculate the population of the town as P(t) where t is the time in years since now. P(t) = 12000(1.05)^t The problem asks for P(12) P(12) = 12000(1.05)^12 P(12) = 12000(1.79585632602) P(12) = [B]21550[/B] <- nearest whole number

A town has a population of 25,000 and grows at 7.7% every 4 months. What will be the population after 6 years? [LIST] [*]1 year = 12 months [*]12 months / 4 months = 3 compounding periods per year [*]3 compounding periods per year * 6 years = 18 compounding periods [/LIST] So we have our population growth as follows: 25,000(1.077)^18 25,000 * 3.8008668804 95,021.67 ~ [B]95,021[/B]

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years. Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods. Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i: P(t) = P * (1 + i)^t Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have: P(8) = 50000 * (1.08)^8 P(8) = 50000 * 1.85093 P(8) = 92,546.51 Since we can't have a partial person, we round down to [B]92,545[/B]

A towns population is currently 500. If the population doubles every 30 years, what will the population be 120 years from now? Find the number of doubling times: 120 years / 30 years per doubling = 4 doubling times Set up our growth function P(n) where n is the number of doubling times: P(n) = 500 * 2^n Since we have 4 doubling times, we want P(4): P(4) = 500 * 2^4 P(4) = 500 * 16 P(4) = [B]8,000[/B]

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would take to grow 85 cm We set up a proportion of cm to years where y is the number of years it takes to grow 85 cm: 35/2 = 85/y To solve this proportion for y, [URL='https://www.mathcelebrity.com/prop.php?num1=35&num2=85&den1=2&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get: [B]y = 4.86[/B]

A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar. Depreciation at 5% means it retains 95% of the value. Set up the depreciation equation to get Book Value B(t) at time t. B(t) = $25,000 * (1 - 0.05)^t Simplifying, this is: B(t) = $25,000 * (0.95)^t The problem asks for B(11) B(11) = $25,000 * (0.95)^11 B(11) = $25,000 * 0.5688 B(11) = [B]$14,220[/B]

A woman dies at the age of 100 and her son is 35 years old how old was she when she gave birth to him. 35 years ago meant she was 100 - 35 = [B]65 years[/B].

A woman whose income for the year was $42,800 paid $10,700 in taxes. What percent of her income did she pay in taxes? Tax Percent = Tax Amount / Income * 100% Tax Percent = $10,700 / $42,800 * 100% Tax Percent = 0.25 * 100% Tax Percent = [B]25%[/B]

a woman's original salary at a business was 3/4 her salary ten years later. If her salary after ten years is $50,000, what was her original salary? 450,000 * 3/4 = [B]$37,500[/B]

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true? The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway. Imagine a third post midway between the two goal posts. It has the same height as the two goalposts. From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

Free Traffic Frenzy: How To Get 450,000 Website Visitors is my 2nd book. It covers 11 years of traffic building tips. I show you all the juicy details and secrets behind the growth of my website to 450,000 monthy visitors...without spending a dime. [URL='https://www.amazon.com/dp/B07BR6G5KC']Check it out on Amazon[/URL].

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities? Assumptions: [LIST] [*]Let years eating be e [*]Let years sleeping be s [/LIST] We're given: [LIST=1] [*]s = e + 24 [*]e + s = 32 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for s: e + e + 24 = 32 To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=e%2Be%2B24%3D32&pl=Solve']type it in our math engine[/URL] and we get: e = [B]4 [/B] Now, we take e = 4 and substitute it into equation (1) to solve for s: s = 4 + 24 s = [B]28[/B]

After 5 years, a car is worth $22,000. It’s value decreases by $1,500 a year, which of the following equations could represent this situation? Group of answer choices Let y be the number of years since 5 years. Our Book value B(y) is: [B]B(y) = 22,000 - 1500y[/B]

After John worked at a job for 10 years, his salary doubled. If he started at $x, his salary after 10 years is _____. Doubled means we multiply by 2, so we have a new salary in 10 years of: [B]2x[/B]

I brute forced this and got a wrong answer, logic tells me is right. I tried the calculator here but maybe messed up the equation using another users problem as an example. Having no luck. Problem: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 9 times the age of Clinton. How old are they now and how old were they 8 years ago?

Let j be Jacob's age and c be Clinton's age. We have: [LIST=1] [*]j = 4c [*]j - 8 = 9(4c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 36c - 72 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D36c-72&pl=Solve']equation solver,[/URL] we get c = 2 Which means j = 4(2) = 8 8 years ago, Jacob was just born. Which means Clinton wasn't even born yet.

she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before? [QUOTE="Drew, post: 1161, member: 63"]she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before?[/QUOTE] oh and my brute force answer was 12-48 and 8 years earlier was 4-40

I read it wrong before. Here you go: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago? [LIST=1] [*]j = 4c [*]j - 8 = 10(c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 10c - 80 [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B]. 8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.

[QUOTE="math_celebrity, post: 1163, member: 1"]I read it wrong before. Here you go: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago? [LIST=1] [*]j = 4c [*]j - 8 = 10(c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 10c - 80 [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B]. 8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.[/QUOTE] Thank you, I see what I did wrong!

The age of the older of the two boys is twice that of the younger. 5 years ago it was three times that of the younger. Find the age of each

A father is three times as old as the son, and the daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63 Find the present age of the father

Ahmed was born in 530 B.C.E. and lived for 60 years, in which year did he die? In B.C.E., the year decreases as time goes on until we get to year 0. So we have the year of death as: 530 - 60 = [B]470 B.C.E.[/B]

Alan is y years old. Beth is 3 years old than Alan.Write an expression for how old Beth is? The word [I]older[/I] means we add 3 to Alan's age of y. So Beth's age is: [B]y + 3[/B]

Alana puts $700.00 into an account to use for school expenses. The account earns 8% interest, compounded annually. How much will be in the account after 4 years? We use our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=4&pl=Annually']balance with interest calculator[/URL] and we get: [B]$958[/B]

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations: [LIST=1] [*]a = b - 3 [*]b = c - 5 [*]a + b + c = 68 [/LIST] Rearrange (2) c = b + 5 Now plug in (1) and (2) revised into (3). We want to isolate for b. a + b + c = 68 (b - 3) + b + (b + 5) = 68 Combine like terms: (b + b + b) + (5 - 3) = 68 3b + 2 = 68 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2B2%3D68&pl=Solve']equation calculator[/URL], and we get b = [B]22[/B]

Alisha is 5 years younger than her brother. If the age of her brother is y years then age of Alisha in terms of her brother Younger means we subtract. If her brother is y years of age, then Alisha is: [B]y - 5[/B]

Allen saves $162 a month. Allen saves $43 less each month than Lane. How much will Lane save in 2 years? [U]Calculate Lane's monthly savings:[/U] Lane's monthly savings = Allen's monthly savings + 43 (since Allan saves 43 less than Lane) Lane's monthly savings = 162 + 43 Lane's monthly savings = 205 1 year = 12 months 2 years = 24 months So we have: Lane's savings in 2 years = Lane's monthly savings * 24 months Lane's savings in 2 years = 205 * 24 Lane's savings in 2 years = [B]4,920[/B]

Allison can pay her gym membership fee monthly but if she pays for her entire year at one she gets a $53 discount her discounted bill at the end of the year was 463 what is her monthly fee Her full annual bill is found by adding the discounted annual bill to the discount amount: Full annual bill = Discounted annual bill + discount amount Full annual bill = 463 + 53 Full annual bill = 516 Her monthly gym membership is found by the following calculation: Monthly Gym Membership = Full Annual Bill / 12 Monthly Gym Membership = 516 / 12 Monthly Gym Membership = [B]$43[/B]

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the entire year is $299, how much will she pay each month? We set up the cost function C(m) where m is the number of months of membership: C(m) = cost per month * m + joining fee Plugging in our numbers from the problem with 12 months in a year, we get: 12c + 35 = 299 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B35%3D299&pl=Solve']type it in our search engine [/URL]and we get: c = [B]22[/B]

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age? Let a be Alvin's age and e be Elga's age. We have the following equations: [LIST=1] [*]a = e - 12 [*]a + e = 60 [/LIST] Plugging in (1) to (2), we get: (e - 12) + e = 60 Grouping like terms: 2e - 12 = 60 Add 12 to each side: 2e = 72 Divide each side by 2 [B]e = 36[/B]

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age? Let a be Alvin's age. Let e be Elga's age. We're given: [LIST=1] [*]a = e - 34 [*]e = 3a [/LIST] Substitute (2) into (1): a = 3a - 34 [URL='https://www.mathcelebrity.com/1unk.php?num=a%3D3a-34&pl=Solve']Typing this equation into the search engine[/URL], we get a = 17 Subtitute this into Equation (2): e = 3(17) e = [B]51[/B]

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=4000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get an accumulated value of 4,960 Interest Paid = Accumulated Value - Principal Interest Paid = 4960 - 4000 Interest Paid = [B]960[/B]

An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died? Set up his life equation per time lived as a boy, youth, man, and old man 1/4 + 1/5 + 1/3 + x = 1. Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=5&pl=LCM']LCM Calculator[/URL], we see the LCM of 3,4,5 is 60. This is our common denominator. So we have 15/60 + 12/60 + 20/60 + x/60 = 60/60 [U]Combine like terms[/U] x + 47/60 = 60/60 [U]Subtract 47/60 from each side:[/U] x/60 = 13/60 x = 13 out of the 60 possible years, so he was [B]60 when he died[/B].

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest number of paintings she can buy and still have a different arrangement every day for the next 41 years? 365 days * 41 years + 10 leap year days = 14,975 days what is the lowest permutations count of n such that nP5 >= 14,975 W[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Permutations']e see that 9P5[/URL] = 15,120, so the answer is [B]9 paintings[/B]

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. If she earns a total of 87400 dollars per year, what is her monthly salary in dollars? Calculate the annual salary without bonus: Annual Salary = Total Pay - Christmas Bonus Annual Salary = 87400 - 6400 Annual Salary = 81000 Now calculate the monthly salary. [I]Note: there are 12 months in a year[/I]: Monthly Salary = Annual Salary / 12 Monthly Salary = 81000/12 [URL='https://www.mathcelebrity.com/fraction.php?frac1=81000%2F12&frac2=3%2F8&pl=Simplify']Monthly Salary[/URL] = [B]6750[/B]

An investment of $200 is now valued at $315. Assuming continuous compounding has occurred for 6 years, approximately what interest rate is needed to be for this to be possible? [URL='https://www.mathcelebrity.com/simpint.php?av=315&p=200&int=&t=6&pl=Continuous+Interest']Using our continuous compounding calculator solving for interest rate[/URL], we get: I = [B]7.57%[/B]

An investor invests $1000. Part of the investment is made at 5% interest and part of the investment is made at 10% interest. How much should be invested at 5% so the total interest in the first year is $80? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=1000&i1=5&i2=10&itot=80&pl=Calculate']split fund interest calculator[/URL], we get: [B]$400[/B]

Ana was y years old 7 years ago. Represent her age twenty years from now twenty years from now, means we add 7 years to get to now and another 20 years to get to twenty years from now: y + 7 + 20 [B]y + 27[/B]

Angie is 11, which is 3 years younger than 4 times her sister's age. Let her sister's age be a. We're given the following equation: 4a - 3 = 11 To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4a-3%3D11&pl=Solve']type this equation into our math engine[/URL] and we get: [B]a = 3.5[/B]

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest? Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits. Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following: [LIST=1] [*]Accumulated Value After 7 years = [B]$101,086.45[/B] [*]Principal = 79,800 [*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B] [/LIST]

Arizona became a state in 1912. This was 5 years after Oklahoma became a state. Which equation can be used to find the year Oklahoma became a state? In what year did Oklahoma become a state? Let o be the year Oklahoma became a state: o = 1912 - 5 o = [B]1907[/B]

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 10 years? Semiannual means twice a year, so 10 years * 2 times per year = 20 periods. We use this and [URL='https://www.mathcelebrity.com/compoundint.php?bal=4000&nval=20&int=2.50&pl=Semi-Annually']plug the numbers into our compound interest calculator[/URL] to get: [B]$5,128.15[/B]

At what simple interest rate will 4500$ amount to 8000$ in 5 years? Simple Interest is written as 1 + it. With t = 5, we have: 4500(1 + 5i) = 8000 Divide each side by 4500 1 + 5i = 1.77777778 Subtract 1 from each side: 5i = 0.77777778 Divide each side by 5 i = 0.15555 As a percentage we multiply by 100 to get [B]15.5%[/B]

Austin deposited $4000 into an account with 4.8% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 4 years? Do not round any intermediate computations, and round your answer to the nearest cent. Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=40000&nval=4&int=4.8&pl=Annually']balance calculator[/URL], we get: [B]$48,250.87[/B]

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years. At any time t, the Bangladesh population at year t is: [B]y = 170,000,000(1.015)^t[/B]

Ben is 3 times as old as Daniel and is also 4 years older than Daniel. Let Ben's age be b, let Daniel's age by d. We're given: [LIST=1] [*]b = 3d [*]b = d + 4 [/LIST] Substitute (1) into (2) 3d = d + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3Dd%2B4&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 2[/B]. Substitute this into equation (1), and we get: b = 3(2) [B]b = 6 [/B] So Daniel is 2 years old and Ben is 6 years old.

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan. Let b be Ben's age and i be Ishaan's age. We're given: [LIST=1] [*]b = 4i [*]b = i + 6 [/LIST] Set (1) and (2) equal to each other: 4i = i + 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4i%3Di%2B6&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]i = 2[/B] Substitute this into equation (1): b = 4(2) [B]b = 8 [/B] [I]Therefore, Ishaan is 2 years old and Ben is 8 years old.[/I]

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now? Let b = Beth's age Let c = Celeste's age We are given: [LIST=1] [*]b = c - 5 [*]b + 1 + c + 1 = 57 [/LIST] Substitute (1) into (2) (c - 5) + 1 + c + 1 = 57 Group like terms: 2c - 3 = 57 [URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B] Substitute c = 30 into Equation (1), we get: b = 30 - 5 [B]b = 25 [/B] Therefore, Beth is 25 and Celeste is 30.

bill is m years old how old will he be in 9 years Since we always get older, we add: [B]m + 9[/B]

Bill is p years old. How old will he be in 10 years? How old was he 5 years ago? [LIST] [*]In 10 years, Bill will be [B]p + 10[/B] [*]5 years ago, Bill was [B]p - 5[/B] [/LIST]

Bill is q years old. How old will he in 6 years ? How old was he 4 years ago ? Start with q years old. In 6 years means we add since it's the future: [B]q + 6[/B] 4 years ago means we subtract since it's in the past: [B]q - 4[/B]

Bonnita deposited $4,500 into a savings account paying 3% interest compounded continuously. She plans on leaving the account alone for 7 years. How much money will she have at that time? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=3&t=7&pl=Continuous+Interest']compound interest calculator[/URL], we get: [B]$5551.55[/B]

Brad has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will he have in 3 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=40&nval=3&int=5&pl=Annually']Using our balance with interest calculator[/URL], we get [B]$46.31[/B].

Brenda invests $1535 in a savings account with a fixed annual interest rate of 3% compounded continuously. What will the account balance be after 8 years Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1535&int=3&t=8&pl=Continuous+Interest']continuous interest balance calculator[/URL], we get: [B]1,951.37 [MEDIA=youtube]vbYV6SYXtvs[/MEDIA][/B]

Bridget deposited $4500 at 6 percent simple interest. How much money was in the account at the end of three years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=6&t=3&pl=Simple+Interest']simple interest balance calculator[/URL], we get: $[B]5,310[/B]

Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bruno Combined age means we add, so we have: 3x + x = 40 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x%2Bx%3D40&pl=Solve']type it in our search engine[/URL] and we get: x = 10 This means Bruno is: 3(10) = [B]30[/B]

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years. Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1500&int=7&t=3&pl=Simple+Interest']simple interest calculator[/URL], the total interest earned over 3 years is [B]$315[/B].

Calculate the value of an investment of $15,000 at 6% interest after 7 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=15000&nval=7&int=6.5&pl=Annually']balance calculator[/URL], we get; [B]23,309.80[/B]

Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent on hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 money than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

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Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: [LIST=1] [*]c = l + 3 <-- older means we add [*]c + l = 63 <-- combined ages mean we add [/LIST] Substitute equation (1) into equation (2): l + 3 + l = 63 Combine like terms to simplify our equation: 2l + 3 = 63 To solve for l, [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D63&pl=Solve']we type this equation into our search engine[/URL] and we get: l = [B]30[/B] Now, we plug l = 30 into equation (1) to solve for c: c = 30 + 3 c = [B]33[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: [LIST=1] [*]c = l + 3 (Since older means we add) [*]c + l = 63 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for c: l + 3 + l = 63 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B3%2Bl%3D63&pl=Solve']type it in our search engine [/URL]and we get: l = [B]30 [/B] Now, we take l = 30 and substitute it in equation (1) to solve for c: c = 30 + 3 c = [B]33[/B]

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than 3 times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year. Let c be the number of cars. Let t be the number of trucks. We're given two equations: [LIST=1] [*]c = 3t + 39000 [*]c + t = 216000 [/LIST] Substitute equation (1) into equation (2) for c: 3t + 39000 + t = 216000 To solve this equation for t, [URL='https://www.mathcelebrity.com/1unk.php?num=3t%2B39000%2Bt%3D216000&pl=Solve']we type it in our math engine [/URL]and we get: t = [B]44,250[/B]

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age Declare variables for each age: [LIST] [*]Let Casey's age be c [*]Let her daughter's age be d [*]Let n be the number of years from now where Casey will be double her daughter's age [/LIST] We're told that: 26 + n = 2(4 + n) 26 + n = 8 + 2n Solve for [I]n[/I] in the equation 26 + n = 8 + 2n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 2n. To do that, we subtract 2n from both sides n + 26 - 2n = 2n + 8 - 2n [SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE] -n + 26 = 8 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 26 and 8. To do that, we subtract 26 from both sides -n + 26 - 26 = 8 - 26 [SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE] -n = -18 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -18/-1 n = [B]18[/B] Check our work for n = 18: 26 + 18 ? 8 + 2(18) 44 ? 8 + 36 44 = 44

Charlene wants to invest $10,000 long enough for it to grow to at least $20,000. The compound interest rate is 6% p.a. How many whole number of years does she need to invest the money for so that it grows to her $20,000 target? We want 10,000(1.06)^n = 20,000. But what the problem asks for is how long it will take money to double. We can use a shortcut called the Rule of 72. [URL='https://www.mathcelebrity.com/rule72.php?num=6&pl=Calculate']Using the Rule of 72 at 6%[/URL], we get [B]12 years[/B].

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them? Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age [LIST=1] [*]a = c + 5 [*]j = a + 6 [*]a + c + j = 31 [*]Rearrange (1) in terms of c: c = a - 5 [/LIST] [U]Plug in (4) and (2) into (3)[/U] a + (a - 5) + (a + 6) = 31 [U]Combine like terms:[/U] 3a + 1 = 31 [U]Subtract 1 from each side[/U] 3a = 30 [U]Divide each side by 3[/U] [B]a = 10[/B] [U]Plug in 1 = 10 into Equation (4)[/U] c = 10 - 5 [B]c = 5[/B] Now plug 1 = 10 into equation (2) j = 10 + 6 [B]j = 16[/B]

Christopher has $25 000 to invest. He finds a bank who will pay an interest rate of 5.65% p.a compounded annually. What will the total balance be after 6 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=6&int=5.65&pl=Annually']compound interest balance calculator[/URL], we get: [B]34,766.18[/B]

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j ) Build an algebraic expression: [B]c = j/2 - 5[/B] <-- Half means we divide by 2 and [I]younger[/I] means we subtract

Cody invests $4,734 in a retirement account with a fixed annual interest rate of 4% compounded continuously. What will the account balance be after 19 years? Using our c[URL='http://www.mathcelebrity.com/simpint.php?av=&p=4734&int=4&t=19&pl=Continuous+Interest']ontinuous interest compounding calculator[/URL], we get: [B]10,122.60[/B]

Condos in Centerville go up in value by 3% each year. If the Ayala family's condo is now worth $697,580, what will it be worth in 2 years? Let the condo value in (y) years be C(y). 3% as a decimal is 0.03, so we have: C(y) = 697,850 * (1.03)^y The problem asks for C(2): C(2) = 697,850 * (1.03)^2 C(2) = 697,850 * 1.0609 C(2) = [B]740.349.07[/B]

Congratulations!! You are hired at Roof and Vinyl Housing Systems. Your starting salary is $45,600 for the year. Each year you stay employed with them your salary will increase by 3.5%. Determine what your salary would be if you worked for the company for 12 years. Set up a function S(y) where y is the number of years after you start at the Roof and Vinyl place. S(y) = 45600 * (1.035)^y <-- Since 3.5% = 0.035 The question asks for S(12): S(12) = 45600 * (1.035)^12 S(12) = 45600 * 1.51106865735 S(12) = [B]68,904.73[/B]

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed that they are much more dangerous than minivans. An owner of a Corvette points out that when statistics are studied, there are far more deaths each year from crashes that involve minivans than crashes that involve Corvettes, so Corvettes, so Corvettes must be safer than minivans. The statistics the Covert owner sites are correct. Is his logic faulty? Why or why not? [B]Faulty.[/B] There are hundreds of times more minivans on the road than Corvettes, so we expect more deaths even if they are the safest car on the road.

Free Cost Recovery Method Calculator - Given a sales price, cost, and set of payments, this determines the gross profit per year based on the cost recovery method.

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Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages Dad's age: y Mom's age (younger means we subtract): y - 5 The total of their ages is found by adding them together: y + y - 5 Group like terms, and we get: [B]2y - 5[/B]

Dan makes 11 an hour working at the local grocery store. Over the past year he has saved 137.50 toward a new pair of retro sneakers. If sneakers cost 240, how many hours will he need to be able to buy the sneakers? Figure out his remaining savings target: 240 - 137.50 = 102.50 Let x equal the number of remaining hours Dan needs to work 11x = 102.50 Divide each side by 11 x = 9.318 We round up for a half-hour to 9.5, or a full hour to 10.

Daniel invests £2200 into his bank account. He receives 10% per year simple interest. How much will Daniel have after 2 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=2200&int=10&t=2&pl=Simple+Interest']simple interest calculator[/URL], we get: [B]$2,640[/B]

Free Date and Time Difference Calculator - Calculates the difference between two dates using the following methods
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Dave has a savings account that pays interest at 3 1/2% per year. His opening balance for May was $1374.67. He did not deposit or withdraw money during the month. The interest is calculated daily. How much interest did the account earn in May? First, determine n, which is 31, since May has 31 days. We use our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1374.67&nval=31&int=3.5&pl=Daily']compound interest balance calculator[/URL] to get: [B]1,378.76[/B]

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Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12. Our givens are: [LIST] [*]I = 450 [*]P = 3000 [*]t = 3 [*]We want r [/LIST] 450 = 3000(r)(3) 450 = 9000r Divide each side by 9000 [B]r = 0.05[/B]

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after 10 years. Round your answer to the nearest penny if necessary. Annual compounding means we don't need to make adjustments to interest rate per compounding period. [URL='https://www.mathcelebrity.com/compoundint.php?bal=9538&nval=10&int=10&pl=Annually']Using our compound interest calculator[/URL], we get our new balance after 10 years of: [B]$24,739.12[/B]

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages. Let d be Dina's age. Let a be Andrea's age. We're given: [LIST=1] [*]d = 2a <-- Twice means multiply by 2 [*]a + d = 72 [/LIST] Substitute equation (1) into equation (2): a + 2a = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B2a%3D72&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]a = 24[/B] Substitute a = 24 into equation (1): d = 2(24) [B]d = 48 So Andrea is 24 years old and Dina is 48 years old[/B]

During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left due to illness. If UPS ended the year with 410 employees, how many did they have at the start of the season? Let x be the number of employees at the start of the season. We have: [LIST] [*]-14 since retiring is an employee loss [*]+122 hired since hiring is an employee gain [*]-31 since illness means a leave [/LIST] x - 14 + 122 - 31 = 410 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-14%2B122-31%3D410&pl=Solve']equation solver[/URL], we get: [B]x = 333[/B]

During your first year on the job, you deposit $2000 in an account that pays 8.5%, compounded continuously. What will be your balance after 35 years? [URL='https://www.mathcelebrity.com/simpint.php?av=&p=2000&int=8.5&t=35&pl=Continuous+Interest']Using our continuous compound balance calculator[/URL], we get a balance of [B]$39,179.25.[/B]

Dwayne wants to start a saving account at his local credit union. If he puts $8000 into a savings account with an annual interest rate of 1.1%, how much simple interest will he have earned after 6 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=8000&int=1.1&t=6&pl=Simple+Interest']simple interest calculator[/URL], we get: $528 of interest earned.

Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 19, 9, 14, 10, 16, 17. Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth. The mean is the average, so we add up the 6 movie scores, and divide by 6. [URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = Sum of 6 Movie Scores / 6 [URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 84 / 6 [URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 14.16666667 The problem asks us to round to the nearest tenth, which is the first decimal place. Since the 2nd decimal place, 6 is more than 5, we round the first decimal place up one and remove the rest. [B]14.2[/B]

Ed invests $5,500 into the stock market which earns 2% per year. In 20 years, how much will Ed's investment be worth if interest is compounded monthly? Round to the nearest dollar. 20 years * 12 months per year = 240 months Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=5550&nval=240&int=2&pl=Monthly']compound interest calculator[/URL], we get: [B]8,276.87[/B]

Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30. What is the greatest age Mary could be? Let e = Emily's age and m = Mary's age. We have the equation e = 2m + 3 and the inequality e + m < 30 Substitute the equation for e into the inequality: 2m + 3 + m < 30 Add the m terms 3m + 3 < 30 Subtract 3 from each side of the inequality 3m < 27 Divide each side of the inequality by 3 to isolate m m < 9 Therefore, the [B]greatest age[/B] Mary could be is 8, since less than 9 [U]does not include[/U] 9.

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site. On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent. a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30. b. Find the 95th percentile, and express it in a sentence. a. P(X >=0.30), calculate the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+0.30&mean=+0.28&stdev=+0.05&n=+1&pl=P%28X+%3E+Z%29']z-score[/URL] which is: Z = 0.4 P(x>0.4) = [B]0.344578 or 34.46%[/B] b. Inverse Normal (0.95) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']calculator[/URL] = 1.644853627 Use NORMSINV(0.95) on Excel 0.28 + 0.05(1.644853627) = [B]0.362242681 or 36.22%[/B]

1. Spend 8000 on a new machine. You think it will provide after tax cash inflows of 3500 per year for the next three years. The cost of funds is 8%. Find the NPV, IRR, and MIRR. Should you buy it? 2. Let the machine in number one be Machine A. An alternative is Machine B. It costs 8000 and will provide after tax cash inflows of 5000 per year for 2 years. It has the same risk as A. Should you buy A or B? 3. Spend 100000 on Machine C. You will need 5000 more in net working capital. C is three year MACRS. The cost of funds is 8% and the tax rate is 40%. C is expected to increase revenues by 45000 and costs by 7000 for each of the next three years. You think you can sell C for 10000 at the end of the three year period. a. Find the year zero cash flow. b. Find the depreciation for each year on the machine. c. Find the depreciation tax shield for the three operating years. d. What is the projects contribution to operations each year, ignoring depreciation effects? e. What is the cash flow effect of selling the machine? f. Find the total CF for each year. g. Should you buy it?

Find the balance if $5000 is invested in an account paying 4.5% interest compounded continuously for 21 years Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=5000&int=4.5&t=21&pl=Continuous+Interest']continuous compounding interest calculator[/URL], we get: [B]$12,864.07[/B]

Find the final amount of money in an account if $ 3,800 is deposited at 8% interest compounded annually and the money is left for 6 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3800&nval=6&int=8&pl=Annually']compound interest with balance calculator[/URL], we get: [B]$6,030.12[/B]

Find the future value and interest earned if $8806.54 is invested for 9 years at 6% compounded (a) semiannually and (b) continuously a) 14,992.54 using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=8806.54&nval=18&int=6&pl=Semi-Annually']balance with interest calculator[/URL] b) 15112.08 using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=8806.54&int=6&t=9&pl=Continuous+Interest']continuous interest balance calculator[/URL]

find the value of $20000 invested for 7 years at an annual interest rate of 2.55% compounded continuously Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=200000&int=2.55&t=7&pl=Continuous+Interest']compound continuous interest with balance calculator[/URL] we get: [B]239.084.58[/B]

Following the birth of triplets, the grandparents deposit $30,000 in a college trust fund that earns 4.5% interest, compounded quarterly. How much will be in the account after 18 years? 18 years = 18 * 4 = 72 quarters. Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=30000&nval=72&int=4.5&pl=Quarterly']compound interest balance calculator[/URL], we have: [B]$67,132.95[/B]

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages? So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next. whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of: [B]6, 8, 10, 12[/B]

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations: [LIST=1] [*]m = d + 25 [*]m = g - 31 [*]d + g + m = 150 [/LIST] This means the daughter is: d = 25 + 31 = 56 years younger than her grandmother. So we have: 4. d = g - 56 Plugging in equation (2) and equation(4) into equation (3) we get: g - 56 + g + g - 31 Combine like terms: 3g - 87 = 150 [URL='https://www.mathcelebrity.com/1unk.php?num=3g-87%3D150&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]g = 79[/B] Plug this into equation (2): m = 79 - 31 [B]m = 48[/B] Plug this into equation (4): d = 79 - 56 [B]d = 23[/B]

Hal bought a house in 1995 for $190,000. If the value of the house appreciates at a rate of 4.5 percent per year, how much was the house worth in 2006 [U]Calculate year difference:[/U] Year Difference = End Year - Start Year Year Difference = 2006 - 1995 Year Difference = 11 Using our [URL='https://www.mathcelebrity.com/apprec-percent.php?q=a+house+worth+190000+appreciates+4.5%25+for+11+years&pl=Calculate+Appreciation']appreciation calculator[/URL], we get the value of the house in 2006: [B]$308,342.08[/B]

Haley invested $750 into a mutual fund that paid 3.5% interest each year compounded annually. Find the value of the mutual fund in 15 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=15&int=3.5&pl=Annually']compound interest calculator[/URL], we get: [B]1,256.51[/B]

Hannah invested $540 in an account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 18 years? [URL='https://www.mathcelebrity.com/simpint.php?av=&p=540&int=4.7&t=18&pl=Continuous+Interest']Using our compound interest balance calculator[/URL], we get: [B]$1,258.37[/B]

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, clothing, and movie tickets. he wants to have more than $100 at the end of summer to make sure he has enough to purchase some new shoes before school starts. how many weeks, w, can harley withdraw money from his savings account and still have more than $100 to buy new shoes? Let the number of weeks be w. Harley needs $100 (or more) for shoes. We have the balance in Harley's account as: 500 - 20w >= 100 To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=500-20w%3E%3D100&pl=Solve']type it in our search engine[/URL] and we get: [B]w <= 20[/B]

Perform a one-sample z-test for a population mean. Be sure to state the hypotheses and the significance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion. Five years ago, the average math SAT score for students at one school was 475. A teacher wants to perform a hypothesis test to determine whether the mean math SAT score of students at the school has changed. The mean math SAT score for a random sample of 40 students from this school is 469. Do the data provide sufficient evidence to conclude that the mean math SAT score for students at the school has changed from the previous mean of 475? Perform the appropriate hypothesis test using a significance level of 10%. Assume that Η = 73.

How many years will it take for an initial investment of $40,000 to go to $60,000? Assuming a rate of interest at 18% compounded continuously [URL='https://www.mathcelebrity.com/simpint.php?av=60000&p=40000&int=18&t=&pl=Continuous+Interest']Using our continuous interest calculator[/URL] and solving for n, we get: n = [B]2.2526 years[/B]

This is a perpetuity with payments assumed at the end of each month. 12% per year = 12/12 = 1% per month The present value of a perpetuity with payments at the end of the month is: Payment/I Plugging in our values, we get: 100/0.01 10,000 [MEDIA=youtube]FFAJnJyAHjw[/MEDIA]

How much money must be invested to accumulate $10,000 in 8 years at 6% compounded annually? We want to know the principle P, that accumulated to $10,000 in 8 years compounding at 6% annually. [URL='https://www.mathcelebrity.com/simpint.php?av=10000&p=&int=6&t=8&pl=Compound+Interest']We plug in our values for the compound interest equation[/URL] and we get: [B]$6,274.12[/B]

How much money will there be in an account at the end of 10 years if $8000 is deposited at a 7.5% annual rate that is compounded continuously? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=8000&int=7.5&t=10&pl=Continuous+Interest']continuous compounding calculator[/URL], we get [B]$16,936[/B].

How much money would you have after 4 years if you invested $550 at 7% annual interest, compounded monthly? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=550&nval=48&int=7.00&pl=Monthly']compound interest calculator, with 4 years * 12 months per year = 48 months as n[/URL], we get: [B]727.13[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 10 years? Assume the account earns 6% interest compounded monthly. We start with a balance of B. We want to know: B(1.06)^10 = 6000 B(1.79084769654) = 6000 Divide each side of the equation by 1.79084769654 to solve for B B = [B]3,350.37[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 15 years? Assume the account earns 8% interest compounded monthly. 8% compounded monthly = 8/12 = 0.6667% per month. 15 years = 15*12 = 180 months We want to know an initial balance B such that: B(1.00667)^180 = $6,000 3.306921B = $6,000 Divide each side by 3.306921 [B]B = $1,814.38[/B]

How old is Ruben if he was 28 years old eleven years ago? Let's Ruben's age be a. If he was 28 years old 11 years ago, then his age is expressed as: a - 11 = 28 [URL='https://www.mathcelebrity.com/1unk.php?num=a-11%3D28&pl=Solve']Plugging this into our calculator[/URL], we get: a = [B]39[/B]

Hunter puts $300.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 10 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=300&nval=10&int=15&pl=Annually']compound interest calculator[/URL], we get: [B]$1,213.67[/B]

I am 12 years old. My brother is 5 years older than me. How old is my brother? Older means we add, so we have: Brother's age = 12 + 5 Brother's age = [B]17[/B]

I invest $3000 at 5% interest a year. So far I have made $600 with simple interest. How many years have I been investing? Simple interest is calculated using interest * principal. We have 5% * 3000 = $150 interest per year We take our $600 of total interest and divide it by our interest per year to get the total years: $600 / $150 = [B]4 years[/B]

The simple interests earned on the sum of money for 4 years at 7.5% p.a. exceeds that on the same sum for 3.5 years at 8% p.a. by $90. (a)Find the original sum of money. (b)If the original sum of money accumulates to $4612.50 in 5 months at simple interest, find the interests rate per annum.

Simple interest = i(n) Using 4 years at 7.5% (0.075), we get: Simple interest = 4(0.075) = 0.3 What is p.a.?

I work 30 hours a week 50 weeks of a year and I earn a salary of 36000 what is my hourly rate 30 hours per week * 50 weeks = 1,500 hours 36000 / 1500 hours = [B]$24 per hour[/B]

if $7000 is invested at 3% compounded monthly, what is the amount after 4 years 4 years = 12 *4 = 48 months since we're compounding monthly. From our c[URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=48&int=3&pl=Monthly']ompound interest calculator,[/URL] we get: [B]$3,381.98[/B]

If $9000 grows to $9720 in 2 years find the simple interest rate. Simple interest formula is Initial Balance * (1 + tn) = Current Balance We have [LIST] [*]Initial Balance = 9000 [*]Current Balance = 9720 [*]n = 2 [/LIST] Plugging in these values, we get: 9000 * (1 + 2t) = 9720 Divide each side by 9000 1 + 2t = 1.08 Subtract 1 from each sdie 2t = 0.08 Divide each side by 2 t = [B]0.04 or 4%[/B]

If 27000 elephants are killed each year, how many elephants would be killed after 13 years? Total Elephants Killed = Elephants Killed per year * Total years Total Elephants Killed = 27,000 * 13 Total Elephants Killed = [B]351,000[/B]

If 3000 is invested at an annual interest rate of 5% and compounded annually, find the balance after 2 years. Use our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=3000&int=5&t=2&pl=Compound+Interest']compound interest calculator[/URL], we get: Balance = [B]$3,307.50[/B]

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 9 years if interest is compounded annually. We assume the interest is compounded at the end of the year. Use the [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=9&i=10&check1=1&pl=Calculate']annuity immediate formula[/URL]: [B]67,897.39[/B]

if a city grows by 12% per month what is the yearly growth rate We know that there are 12 months in a year. 12% = 0.12 Annual Growth Rate = (1 + Monthly Growth Rate)^12 - 1 Annual Growth Rate = (1 + 0.12)^12 - 1 Annual Growth Rate = (1.12)^12 - 1 Annual Growth Rate = 3.89597599255 - 1 Annual Growth Rate = 2.90 For our percentage, our annual growth rate is the Annual growth rate * 100% 2.90 * 100% = [B]290%[/B]

If a person invests $360 In an account that pays 8% interests compounded annually, find the balance after 5 years [B]$528.95[/B] per our [URL='http://www.mathcelebrity.com/intbal.php?startbal=360&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2005&pl=Annual+Credit']balance calculator[/URL].

if a teachers salary grows by 4% each year. How many years will it take to double. We can use the[URL='https://www.mathcelebrity.com/rule72.php?num=4&pl=Calculate+Rule+of+72+Time'] Rule of 72 at 4%[/URL] to get [B]18 years[/B]

If Hailey makes $300 every two weeks, how much will Hailey have at the end of the year? 52 weeks in a year, which means we have: 52/2 = 26 two week periods 300 * 26 two week periods = [B]7,800[/B]

If Susie is 14, what was her age x years ago? x years ago means we subtract x from 14: [B]14 - x[/B]

If the probability of getting struck by lighting each year is 1 in 1,000,000, what is the probability that you will not be struck by lightning in one year? Our sample space is either getting struck by lightning or NOT getting struck by lightning. So we have: P(Not getting struck by lightning) = 1 - P(Getting struck by lightning) P(Not getting struck by lightning) = 1 - 1/1,000,000 P(Not getting struck by lightning) = [B]999,999/1,000,000[/B]

If Tom makes 2.9 million dollars a day how much would he make in a decade 2.9 million dollars per day * 365 days per year * 10 years in a decade = [B]10,585,000,000[/B]

If you have $15,000 in an account with a 4.5% interest rate, compounded quarterly, how much money will you have in 25 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=15000&nval=100&int=4.5&pl=Quarterly']Using our compound interest calculator[/URL] with 25 years * 4 quarters per year = 100 periods of compounding, we get: [B]$45,913.96[/B]

If you save $110 in one month, how much will you save in one year? 110 per month * 12 months in a year = [B]1,320 saved in a year[/B]

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average? Batting Average = Hits / Times at Bat Batting Average = 195 / 600 [URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Batting Average[/URL] = [B]0.327[/B]

In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age today be a. We're given: a + 16 = 3a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B16%3D3a&pl=Solve']Type this equation into the search engine[/URL], and we get: a = [B]8[/B]

In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age right now be b. We have, in 16 years, Ben's age will be 3 times what his age is now: b + 16 = 3b Subtract b from each side: 2b = 16 Divide each side by 2 [B]b = 8[/B] Check our work: 16 years from now, Ben's age is 8 + 16 = 24 And, 8 x 3 = 24

In 1910, the population of math valley was 15,000. If the population is increasing at an annual rate of 2.4%, what was the population in 1965? 1965 - 1910 = 55 years of growth. P(1965) = 15,000 * (1.024)^55 P(1965) = 15,000 * 3.68551018049 P(1965) = 55282.652707 ~ [B]55,283[/B]

In 20 years charles will be 3 times as old as he is now. How old is he now? Let Charles's age be a today. We're given: a + 20 = 3a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B20%3D3a&pl=Solve']If we type this equation into our search engine[/URL], we get: [B]a = 10 [/B] Let's check our work in our given equation: 10 + 20 ? 3(10) 30 = 30 <-- Checks out!

In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010? In 5 years, the book appreciated 205 - 125 = 80 in value. 80/5 = 16. So each year, the book increases 16 in value. Set up the cost function: [B]C(y) = 16y where y is the number of years since 2010[/B]

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4% each year since. Let x = the number of years since 2010 and y = the population of Greenbow. What will the population of Greenbow be in 2022? P(x) = 1,100(1.04)^x x = 2022 - 2010 x = 12 years We want P(12): P(12) = 1,100(1.04)^12 P(12) = 1,100(1.60103221857) P(12) = [B]1,761.14 ~ 1,761[/B]

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% each year. What is the geese population in 2022? 12% is also 0.12. We have the population growth function: P(t) = 750(1.12)^t 2022 - 2016 is 6 years of growth. We want P(6). P(6) = 750(1.12)^6 P(6) = 750(1.9738) [B]P(6) = 1,480.36 ~ 1,480[/B]

In 2016, National Textile installed a new textile machine in one of its factories at a cost of $300,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000. (a) Find an expression for the textile machines book value in the t th year of use (0 ≤ t ≤ 10) We have a straight line depreciation. Book Value is shown on the [URL='http://www.mathcelebrity.com/depsl.php?d=&a=300000&s=10000&n=10&t=3&bv=&pl=Calculate']straight line depreciation calculator[/URL].

In 45 years, Gabriela will be 4 times as old as she is right now. Let a be Gabriela's age. we have: a + 45 = 4a Subtract a from each side: 3a = 45 Divide each side by a [B]a = 15[/B]

in 5 years, sarah will be old enough to vote in an election. the minimum age for voting is at least 18 years. what can you say about how old she is now? 18 - 5 = [B]13 years old[/B]

In 56 years, Stella will be 5 times as old as she is right now. Let Stella's age be s. We're given: s + 56 = 5s [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]s = 14[/B]

In 8 years kelly's age will be twice what it is now. How old is kelly? Let Kelly's age be a. In 8 years means we add 8 to a: a + 8 Twice means we multiply a by 2: 2a The phrase [I]will be[/I] means equal to, so we set a + 8 equal to 2a a + 8 = 2a To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D2a&pl=Solve']type it in our math engine[/URL] and we get: a = [B]8 [/B] [U]Evaluate a = 8 and check our work[/U] 8 + 8 ? 2(8) 16 = 16 [MEDIA=youtube]y4jaQpkaJEw[/MEDIA]

In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days, and unhealthy air quality 4% of the days. How many days per year do residents have unhealthy air quality? 4% of 365 days in a year = [B]14.6 days. If we are talking full days, we have 14.[/B]

In a newspaper, it was reported that yearly robberies in Springfield were up 34% to 134 in 2011 from 2010. How many robberies were there in Springfield in 2010? 2010 robberies = 2011 robberies / 1.34 2010 robberies = 134 / 1.34 2010 robberies = [B]100[/B]

In a newspaper, it was reported that yearly robberies in Springfield were up 40% to 77 in 2012 from 2011. How many robberies were there in Springfield in 2011? Let r be the number of robberies in 2011. We have: Robberies in 2012 = Robberies in 2011 * 1.4 77 = r * 1.4 Divide each side by 1.4 [B]r = 55[/B]

In a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 from 2012. How many robberies were there in Springfield in 2012? Let the robberies in 2012 be r. We're given the following equation: 1.5r = 351 <-- We write a 50% increase as 1.5 To solve this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.5r%3D351&pl=Solve']type it into our search engine[/URL] and we get: r = [B]234[/B]

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]5575[/B]

In the past year, Yoko watched 76 movies that she thought were very good. She watched 80 movies over the whole year. Of the movies she watched, what percentage did she think were very good? [URL='http://www.mathcelebrity.com/perc.php?num=76&den=80&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Enter 76/80 into our search engine to get 95%[/URL].

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980? Age in 1980: [LIST] [*]Let Michael's age be m [*]Nancy's age is 2m [*]Rick's age is 2 * 2m = 4m [/LIST] Age in 1992: [LIST] [*]Michael's age = m + 12 [*]Nancy's age is 2m + 12 [*]Rick's age is 2 * 2m = 4m + 12 [/LIST] Total them up: m + 12 + 2m + 12 + 4m + 12 = 78 Solve for [I]m[/I] in the equation m + 12 + 2m + 12 + 4m + 12 = 78 [SIZE=5][B]Step 1: Group the m terms on the left hand side:[/B][/SIZE] (1 + 2 + 4)m = 7m [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 12 + 12 + 12 = 36 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 7m + 36 = + 78 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 36 and 78. To do that, we subtract 36 from both sides 7m + 36 - 36 = 78 - 36 [SIZE=5][B]Step 5: Cancel 36 on the left side:[/B][/SIZE] 7m = 42 [SIZE=5][B]Step 6: Divide each side of the equation by 7[/B][/SIZE] 7m/7 = 42/7 m = 6 Rick's age = 6 * 4 = [B]24 [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B12%2B2m%2B12%2B4m%2B12%3D78&pl=Solve']Source[/URL] [/B]

In the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan's age was n, how old were Rachel and Luke? Rachel's age = 3 * Dan's age Rachel's age = 3n Luke's age = 3 times Rachel's age Luke's age = 3(3n) Luke's age = [B]9n[/B]

In the year 1999, Hicham El Guerrouj of Morocco set a new world record when he ran a mile in 3 minutes 43.13 seconds. What was his speed in miles per hour? (Round your answer to the nearest hundredth.) 3 minutes = 60 seconds per minute = 180 seconds 180 seconds + 43.13 seconds = 223.13 seconds 223.13 seconds/3600 seconds per hour = 1 mile/n miles Cross multiply: 223.13n = 3600 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=223.13n%3D3600&pl=Solve']equation solver[/URL], we get: n = [B]16.13 miles per hour[/B]

In the year 2000, the population of Rahway, New Jersey, was 26500. Express this number in scientific notation 26,500 in [URL='https://www.mathcelebrity.com/scinot.php?num=26500&pl=Convert+to+Number']scientific notation is found using our scientific notation calculator[/URL]: [B]2.65 x 10^4[/B]

In x years time, Peter will be 23 years old. How old is he now? Let Peter's current age be a. In x years time means we add x to a, so we're given: a + x = 23 We want to find a, s we subtract x from each side to get: a + x - x = 23 - x Cancel the x terms on the left side and we get: a = [B]23 - x[/B]

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William? [U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U] i = 72+y w = 4+y [U]We want the time for Ishaan age will be 5 times William's age:[/U] i = 5w 72 + y = 5(4 + y) We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get: y = [B]13[/B] [/SIZE]

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation? Let y be the number of years since Jack bought the car. We have a Book value B(y): [B]B(y) = 17500 - 750y[/B]

Jacob bought a car that loses 10% of its value each year. If the original cost of the car is n dollars, what is its value after 3 years? [LIST] [*]Year 1: 0.9*n = 0.9n [*]Year 2: 0.9 * 0.9n = 0.81n [*]Year 3: 0.9 * 0.81n = [B]0.729n[/B] [/LIST]

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula to compute a mortgage payment, M, is shown below, where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Janice's bank offers a monthly interest rate of 0.325% for a 12-year mortgage. How many monthly payments must Janice make? 12 years * 12 months per year = [B]144 mortgage payments[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number. Calculate earnings per lifespan: Earnings per lifespan = lifespan in years * Annual Earnings Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year) Earnings per lifespan = 8,085,480 Calculate the number of lifespans needed to match Jeff Bezos earnings: Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan Number of lifespans = 143,100,000,000 / 8,085,480 Number of lifespans = [B]17,698.39 ~ 17,699[/B]

Jeremy is x years old now. How old is he 10 years from now? We add 10 years to Jeremy's current age of x: [B]x + 10[/B]

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work? We know that there are 12 months in a year. Percentage worked = Months worked in a year / months in a year * 100% Percentage worked = 7/12 * 100% Percentage worked = 0.5833333 * 100% Multiplying by 100 means we shift the decimal place 2 spaces to the right: Percentage worked = [B]58.33%[/B]

Jessie invests $3345 in the stock market. Over the 3 years she has this invested she gets an average return of 7.8%. How much will her investment be worth after the 3 years? 7.8% = 0.078, so we use our compound interest formula to find our balance after 3 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3345&nval=3+&int=7.8&pl=Annually']compound interest balance calculator[/URL], we get: [B]$4,190.37[/B]

Jessie works in a hat shop for 4 hours per day. She worked a total of 592 hours over the past year. How many days did she turn up for work? Days worked = Total Hours Worked / Hours worked per day Days worked = 592/4 Days worked = [B]148 days[/B]

Jim invested $25,000 at an interest rate of 2% compounded anually. Approximately how much would Jim’s investment be worth after 2 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=20&int=2.0&pl=Annually']compound interest calculator[/URL], we get: [B]$37,148.68[/B]

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations: [LIST=1] [*]j + a + u = 82 [*]j = u + 9 [*]a = u - 8 [/LIST] Substitute (2) and (3) into (1) (u + 9) + (u - 8) + u = 82 Combine Like Terms: 3u + 1 = 82 [URL='https://www.mathcelebrity.com/1unk.php?num=3u%2B1%3D82&pl=Solve']Type this equation into the search engine[/URL], and we get u = 27. The eldest (oldest) of the 3 is Jim. So we have from equation (2) j = u + 9 j = 27 + 9 [B]j = 36[/B]

Jocelyn invested $3,700 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money would be in the account after 6 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=3700&int=1.5&t=6&pl=Continuous+Interest']continuous interest with balance calculator[/URL], we get: [B]$4,048.44[/B]

Joey puts $1,000.00 into an account to use for school expenses. The account earns 12% interest, compounded annually. How much will be in the account after 6 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1000&nval=6&int=12&pl=Annually']balance calculator[/URL], we get [B]$1,973.82[/B]

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time? 10 years ago means we [I]subtract[/I] 10 from n: [B]n - 10[/B] 20 years time or 20 years from now means we [I]add[/I] 20 to n: [B]n + 20[/B]

John is y years old. Sarah is 9 years older than John. How old is Sarah Older means we add, so we have Sarah's age s as: s = [B]y + 9[/B]

John's age 4 years ago, if he will be y years old in 5 years. Josh's age now is y - 5 Josh's age 4 years ago is y - 5 - 4 = [B]y - 9[/B]

Jonathan was thrilled when his boss told him he was going to get a .5% raise. If Jonathan currently paid $10,000 per year, how much of a raise will he get? 0.5% = 0.005 10,000 * 0.005 = [B]$50[/B]

Joshua deposited $1200 into his two bank accounts. How much did he put in his savings account, which pays 9% per year in interest, and his chequing account, which pays 4% per year, if he earned $88 in interest after one year? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=1200&i1=9&i2=4&itot=88&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*][B]800 in savings[/B] [*][B]400 in checking[/B] [/LIST]

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die? BC means "Before Christ". On a timeline, it represents a negative number, where year 0 is the birth of Christ. So we have -100 + 66 = -34 -34 means [B]34 BC[/B].

Kathy rans 16 miles a week. If she continues to ran at this rate how many miles will she ran in a year? 52 weeks / year * 16 miles / week = [B]832 miles /year[/B]

Kendra has $20 in a savings account. The interest rate is 10%, compounded annually. To the nearest cent, how much will she have in 2 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=20&nval=2&int=10&pl=Annually']balance with interest calculator[/URL], we get [B]$24.20[/B].

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they? Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given: [LIST=1] [*]k = 0.5m [*]k = l - 3 [*]k + l + m = 39 [/LIST] Rearranging (1) by multiplying each side by 2, we have: m = 2k Rearranging (2) by adding 3 to each side, we have: l = k + 3 Substituting these new values into (3), we have: k + (k + 3) + (2k) = 39 Group like terms: (k + k + 2k) + 3 = 39 4k + 3 = 39 [URL='https://www.mathcelebrity.com/1unk.php?num=4k%2B3%3D39&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]k = 9 [/B] Substitute this back into (1), we have: m = 2(9) [B]m = 18 [/B] Substitute this back into (2), we have: l = (9) + 3 [B][B]l = 12[/B][/B]

Kent Realty Company had an annual loss of $63,408. What was the average loss per month? Convert years to months 1 year = 12 months 63,408/12 = [B]5,284 per month[/B]

Kevin borrowed $8000 at a rate of 7.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 10 years? We want to find 8,000(1.075)^10 Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=10&int=7.5&pl=Annually']balance calculator[/URL], we get: [B]$16,488.25[/B]

Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: [LIST=1] [*]k = 4d [*]k = d + 6 [/LIST] Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6 Divide each side by 3: 3d/3 = 6/3 Cancel the 3 on the left side: d = 2 Plug this back into equation (1): k = 4(2) k = 8 So Daniel is 2 years old and Kevin is 8 years old

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age? Let k be Kiko's present age Let s be Kiko's sisters age. We're given two equations: [LIST=1] [*]k = 6s [*]k + 6 = 3(s + 6) [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for k: 6s + 6 = 3(s + 6) [URL='https://www.mathcelebrity.com/1unk.php?num=6s%2B6%3D3%28s%2B6%29&pl=Solve']Typing this equation into our math engine[/URL] to solve for s, we get: s = [B]4[/B] To solve for k, we substitute s = 4 into equation (1) above: k = 6 * 4 k = [B]24[/B]

Kunio puts $2,200.00 into savings bonds that pay a simple interest rate of 2.4%. How much money will the bonds be worth at the end of 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=2200&int=2.4&t=4&pl=Simple+Interest']simple interest balance calculator[/URL], we his account will be worth [B]$2,411.20[/B] after 4 years

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate. Let x be the amount invested at 6%. Then 31000 - x is invested at 7%. We have the following equation: 0.06x + (31000 - x)0.07 = 2090 Simplify: 0.06x + 2170 - 0.07x = 2090 Combine like Terms -0.01x + 2170 = 2090 Subtract 2170 from each side -0.01x = -80 Divide each side by -0.01 x = [B]8000 [/B]at 6% Which means at 7%, we have: 31000 - 8000 = [B]23,000[/B]

Last year I made $50,000 working for a company. This year everyone takes a 9% pay cut. Next year everyone is promised a 15% pay raise. How much will I make next year? [U]Calculate pay cut amount with 9% = 0.09:[/U] Pay cut amount = Current Salary * (1 - pay cut percent) Pay cut amount = 50000 * (1 - 0.09) Pay cut amount = 50000 * 0.91 Pay cut amount = 45500 [U]Calculate pay raise with 15% = 0.15[/U] Pay raise amount = Pay Cut Salary * (1 + pay raise percent) Pay raise amount = 45500 * (1 + 0.15) Pay raise amount = 45500 * 1.15 Pay raise amount = [B]52,325[/B]

Last year, Eric had $20,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $1880 in interest. How much did he invest in each account? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=20000&i1=10&i2=7&itot=1880&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]Fund 1 = 16,000[/B] [*][B]Fund 2 = 4,000[/B] [/LIST]

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the total number of miles he biked. We add both years to get our algebraic expression of miles biked: [B]m + 524[/B]

Last year, Manuel had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account? The answer is $9,000 and $1,000 found on [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=10000&i1=7&i2=10&itot=730&pl=Calculate']this calculator[/URL].

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for the total number of miles she biked. [U]Calculate Total miles biked[/U] Total miles biked = Last Year + This year Total miles biked = [B]m + 390[/B]

Last year, Miguel had $10,000 to invest. He invested some of it in an account that paid 5% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $800 in interest. How much did he invest in each account? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=10000&i1=5&i2=10&itot=800&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]4,000 in Fund 1 at 5%[/B] [*][B]6,000 in Fund 2 at 10%[/B] [/LIST]

Last year, Susan interviewed 240 people. How many each month? 240 people / yr * 1 yr / 12 months = 240 people / 12 months = [B]20 people per month[/B]

Last year, the 6th grade had 200 students. This year the number decreased 35% How many students are in this year's 6th grade class? [URL='https://www.mathcelebrity.com/percentoff.php?p1=&m=35&p2=200&pl=Calculate']200 decreased by 35%[/URL] is [B]130[/B]

Lauren invested $340 in an account paying an interest rate of 5.8% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years? 13 years * 12 months per year = 156 compounding periods. [URL='https://www.mathcelebrity.com/compoundint.php?bal=340&nval=156&int=5.8&pl=Monthly']Using our compound interest balance calculator[/URL] with 156 for t, we get: $[B]721.35[/B]

Leah is 12 years older than Anna. if the age of Anna is x, what is the age of Leah? Older means we add 12 to Anna's age. So if Anna's age is x, then Leah's age (l) is: l = [B]x + 12[/B]

Lei is 15 years old, represent her age m years ago years ago means we subtract: [B]15 - m[/B]

Let x be the dog’s age in years. What is the dog’s age when he is thrice as old? Thrice means triple, or multiply by 3. So we have the future age as: [B]3x[/B]

let x be the variable, an age that is at least 57 years old At least means greater than or equal to x >= 57

Levi invested $630 in an account paying an interest rate of 4.6% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $970? 3,425 days, per the [URL='http://www.mathcelebrity.com/compoundint.php?bal=630&nval=3425&int=4.6&pl=Daily']balance calculator[/URL].

Lily put $750 in the bank if she earns 4% interest how much will she have in 5 years? We assume annual compounding, so [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=5&int=4&pl=Annually']using our balance with compound interest calculator[/URL], we have: [B]$912.49[/B]

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,000. To the nearest hundred dollars, estimate her profits for 2011. Calculate the number of years of appreciation: Appreciation years = 2011 - 2002 Appreciation years = 9 So we want 30000 to grow for 9 years at 6%. We [URL='https://www.mathcelebrity.com/apprec-percent.php?num=30000togrowfor9yearsat6%.whatisthevalue&pl=Calculate']type this into our search engine[/URL] and we get: [B]$50,684.37[/B]

Lino worked in Singapore for 60 months How many years did he work in Singapore? 60 months / 12 months per year = [B]5 years[/B]

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew? Let the age of Logan's nephew be n. We're given: 4n + 8 = 32 (Since [I]older[/I] means we add) To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get: [B]n = 6[/B]

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent? This is an annuity due, since the first payment is made on the date of purchase. Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/B].

Luke invested $140 at 6% simple interest for a period of 7 years. How much will his investment be worth after 7 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=140&int=6&t=7&pl=Simple+Interest']simple interest balance calculator[/URL], we get [B]$198.80[/B].

Luke invested 120 at 5% simple interest for a period of 7 years. How much will investment be worth after years Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=120&int=5&t=7&pl=Simple+Interest']balance with simple interest calculator[/URL], we get: [B]162[/B]

Manuel can pay for his car insurance on a monthly basis, but if he pays an entire year's insurance in advance, he'll receive a $40 discount. His discounted bill for the year would then be $632. What is the monthly fee for his insurance? His full bill F, is denoted as: F - 40 = 632 [URL='https://www.mathcelebrity.com/1unk.php?num=f-40%3D632&pl=Solve']If we add 40 to each side[/URL], we get: F = [B]$672[/B]

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry. Let m be Martha's age. Let h be Harry's age. We're given two equations: [LIST=1] [*]m = h + 18 [I](older means we add)[/I] [*]h + m = 106 [/LIST] Substitute equation (1) into equation (2) for m: h + h + 18 = 106 To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get: h = [B]44[/B]

Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother? Let her brother's age be b. We're given: 2b/3 = 24 To solve this proportion for b, [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=24&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get: b = [B]36[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be? Let m be Marty's age and w be Warren's age. We have two equations: (1) m = 6w - 3 (2) m + w > 11 Plug (1) into (2) 6w - 3 + w > 11 Combine w terms 7w - 3 > 11 Add 3 to each side 7w > 14 Divide each side by 7 w > 2 which means [B]w = 3[/B] as the youngest age.

Mary invested $800, part at 9% per annum and the rest at 12% per annum. After 1 year, the total interest earned was $79.50. How much did she invest at each rate? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=800&i1=9&i2=12&itot=79.50&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*]Fund 1: $550 [*]Fund 2: $250 [/LIST]

Mary is x years old. How old will she be in 9 years? How old was she 8 years ago In 9 years, we add, since her age goes up, so she'll be: [B]x + 9 [/B] 8 years ago, we subtract, since her age goes down, so she'll be: [B][B]x - 8[/B][/B]

Match each variable with a variable by placing the correct letter on each line. a) principal b) interest c) interest rate d) term/time 2 years 1.5% $995 $29.85 [B]Principal is $995 Interest is $29.85 since 995 * .0.15 * 2 = 29.85 Interest rate is 1.5% Term/time is 2 year[/B]s

Matthew has $3,000 in a savings account that earns 10% interest per year. How much will he have in 3 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=3&int=10&pl=Annually']compound interest with balance calculator[/URL], we get: [B]$3,993[/B]

Max is 23 years younger than his father.Together their ages add up to 81. Let Max's age be m, and his fathers' age be f. We're given: [LIST=1] [*]m = f - 23 <-- younger means less [*]m + f = 81 [/LIST] Substitute Equation (1) into (2): (f - 23) + f = 81 Combine like terms to form the equation below: 2f - 23 = 81 [URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]f = 52[/B] Substitute this into Equation (1): m = 52 - 23 [B]m = 29[/B]

Max was 25 years old in 2011 what year was he born? Year of Birth = Year - Age in Year Year of Birth = 2011 - 25 Year of Birth = [B]1986[/B]

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad? Let Max's father be age f. We're given: (f + 2)/4 = 13 Cross Multiply: f + 2 = 52 [URL='https://www.mathcelebrity.com/1unk.php?num=f%2B2%3D52&pl=Solve']Typing this equation into the search engine[/URL], we get: f = [B]50[/B]

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales. Last year she sold 344000 worth of products. What percent of her total income was her commission? Calculate Melinda's commission: 344,000 * 0.05 = 17,200 Calculate her total income for the year Total Income = Base Pay + Commission Total Income = 17,000 + 17,200 Total Income = 34,200 Calculate the percent of her income which is commission: Commission Income Percent = 100 * 17,200/34,200 Commission Income Percent = 100 * 0.5029 [B]Commission Income Percent = 50.29%[/B]

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable “m” to represent the number of months that you use the app. Set up the cost function C(m) where m is the number of months you subscribe: C(m) = Monthly Subscription Fee * months + Purchase fee [B]C(m) = 2.99m + 5[/B]

Mr. Elk is secretly a huge fan of Billie Eilish, and is saving up for front row seats. He puts $250 in the bank that has an interest rate of 8% compounded daily. After 4 years, Billie is finally hitting up NJ on her tour. How much money does Mr. Elk have in the bank? (rounded to the nearest cent) * 4 years = 365*4 days 4 years = 1,460 days. Using this number of compounding periods, we [URL='https://www.mathcelebrity.com/compoundint.php?bal=250&nval=1460&int=8&pl=Daily']plug this into our compound interest calculator[/URL] to get: [B]$344.27[/B]

Mr. Johnson earned $16,000 in 4 months. At this rate, how much money did he earn in one year? $16,000 / 4 months * 12 months / year = [B]$48,000 per year[/B]

Mr. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 of his age. If Mr. Tan’s age is 60, how old are his elder and youngest daughter? Let Mr. Tan's age be a. We're given: [LIST] [*]Elder Daughter's age = 60/3 = [B]20 years old[/B] [*]Younger Daughter's age = 60/4 = [B]15 years old[/B] [/LIST]

Ms. Gonzales is investing $17000 at an annual interest rate of 6% compounded continuously. How much money will be in the account after 16 years? Round your answer to the nearest hundredth (two decimal places). Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=17000&int=6&t=16&pl=Continuous+Interest']continuous interest calculator[/URL], we get: [B]44,398.84[/B]

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is my brother Brother's age is x: I am 5 years older, meaning I'm x + 5: The combined age is found by adding: x + (x + 5) = 30 Group like terms: 2x + 5 = 30 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]12.5[/B]

1/2 of the parent age is 34/2 = 17. 9 less than that is 17 - 9 = 8. The son is 8 years old. You can also write this as 1/2(34) - 9 --> 17 - 9 = 8.

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter? Declare variables for each age: [LIST] [*]Let Nancy's age be n [*]Let her daughter's age be d [/LIST] We're given two equations: [LIST=1] [*]n = 3d - 10 [*]n = 41 [/LIST] We set 3d - 10 = 41 and solve for d: Solve for [I]d[/I] in the equation 3d - 10 = 41 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 41. To do that, we add 10 to both sides 3d - 10 + 10 = 41 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 3d = 51 [SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE] 3d/3 = 51/3 d = [B]17[/B]

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I] [I][/I] Set up the Account equation A(w) where w is the number of weeks that pass. Nancy (we add since savings means she accumulates [B]more[/B]): A(w) = 25w + 435 Shane (we subtract since spending means he loses [B]more[/B]): A(w) = 875 - 15w Set both A(w) equations equal to each other to since we want to see what w is when the account are equal: 25w + 435 = 875 - 15w [URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get: w =[B] 11[/B]

Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer would give her $10,200 plus a prize pig. After working for 5 months, Natalie decided to quit. The farmer determined that 5 months of work was equal to $3375 plus the pig. How much money was the pig worth? The value of a year's work is $10,200 plus a pig of unknown value. The farmer took away $6825 because Natalie worked 5 months. If Natalie worked 7 more months, she would have been paid the additional $6825. 6825/7 months work = $975 per month A full year's work is $975 * 12 = $11,700 Pig value = Full years work - payout Pig value = 11,700 - 10,200 Pig value = [B]1,500[/B]

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava? Let Nava's age be n and Edward's age be e. We have 2 equations: [LIST=1] [*]n = e + 17 [*]n + e = 29 [/LIST] Substitute (1) into (2) (e + 17) + e = 29 Group like terms: 2e + 17 = 29 Running this equation [URL='http://www.mathcelebrity.com/1unk.php?num=2e%2B17%3D29&pl=Solve']through our search engine[/URL], we get: e = 6 Substitute this into equation (1) n = 6 + 17 [B]n = 23[/B]

Nia is trying to decide between two possible jobs. Job A pays $2000 a month with a 2% annual raise. Job B pays 24,000 a year with a $500 annual raise. Write a function to represent the annual salary for Job A after x years. Write a function to represent the annual salary for Job B after x years. After how many years would Nia have a greater salary at Job A? Nia Job A salary at time t: S(t) $2,000 per month equals $24,000 per year. So we have S(t) = 24,000(1.o2)^t Nia Job B salary at time t: S(t) $24,000 per year. So we have S(t) = 24,000 + 500t We want to know t when Job A salary is greater than Job B Salary: 24,000(1.o2)^t > 24,000 + 500t Time | A | B 0 | 24000 | 24000 1 | 24480 | 24500 2 | 24969.6 | 25000 3 | 25468.99 | 25500 4 | 25978.37 | 26000 5 | 26497.94 | 26500 6 | 27027.9 | 27000 7 | 27568.46 | 27500 8 | 28119.83 | 28000 9 | 28682.22 | 28500 10 | 29255.87 | 29000 11 | 29840.98 | 29500 12 | 30437.8 | 30000 13 | 31046.56 | 30500

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years? Let n be Nicole's age. Let d be Donald's age. We're given two equations: [LIST=1] [*]n = 0.5d [*]n + d = 72 [/LIST] Substitute equation (1) into (2): 0.5d + d = 72 1.5d = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=1.5d%3D72&pl=Solve']Typing this equation into the search engine and solving for d[/URL], we get: d = [B]48[/B]

Nio is 20 years old and his brother Miguel is 8 years old. How old was Miguel when Nio is only 15? Nio is 20. 20 - 15 is 5 years ago. So Miguel's age 5 years ago is: 8 - 5 = [B]3[/B]

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent. [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get: A = [B]1,521.96[/B]

On January 1st a town has 75,000 people and is growing exponentially by 3% every year. How many people will live there at the end of 10 years? [URL='https://www.mathcelebrity.com/population-growth-calculator.php?num=atownhasapopulationof75000andgrowsat3%everyyear.whatwillbethepopulationafter10years&pl=Calculate']Using our population growth calculator[/URL], we get: [B]100,794[/B]

On Melissa 6 birthday she gets a $2000 cd that earns 4% interest, compounded semiannual. If the cd matures on her 16th birthday, how much money will be available? Semiannual compounding means twice a year. With 16 - 6 = 10 years of compounding, we have: 10 x 2 = 20 semiannual periods. [URL='https://www.mathcelebrity.com/compoundint.php?bal=2000&nval=20&int=4&pl=Semi-Annually']Using our interest on balance calculator[/URL], we get: [B]$2,971.89[/B]

Paul’s age is 7 years younger than half of Marina’s age. Express their ages. Assumptions: [LIST] [*]Let Paul's age be p [*]Let Marina's age be m [/LIST] Our expression is: [B]p = 1/2m - 7[/B]

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number. We have the equation y(x): y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97 The problem asks for y(2020). So x = 2020 - 2010 = 10. y(10) = 25,000(0.97)^10 y(10) = 25,000(0.73742412689) y(10) = [B]18,435.60[/B]

People with a drivers license are at least 16 years old and no older than 85 years old. Set up the inequality, where p represents the people: [LIST=1] [*]The phrase [I]at least[/I] means greater than or equal to. So we use the >= sign. 16 <= p [*]The phrase [I]no older than[/I] means less than or equal to. So we use the <= sign. p <= 85 [/LIST] Combine these inequalities, and we get: [B]16 <= p <= 85[/B] To see the interval notation for this inequality and all possible values, visit the [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=16%3C%3Dp%3C%3D85&pl=Show+Interval+Notation']interval notation calculator[/URL].

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200? Set P(t) = 19,200 0.7t^2+6t+15,000 = 19,200 Subtract 19,200 from each side: 0.7t^2+6t+4200 = 0 The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B] t 0.7t^2 6t Add 15000 Total 1 0.7 6 15000 15006.7 2 2.8 12 15000 15014.8 3 6.3 18 15000 15024.3 4 11.2 24 15000 15035.2 5 17.5 30 15000 15047.5 6 25.2 36 15000 15061.2 7 34.3 42 15000 15076.3 8 44.8 48 15000 15092.8 9 56.7 54 15000 15110.7 10 70 60 15000 15130 11 84.7 66 15000 15150.7 12 100.8 72 15000 15172.8 13 118.3 78 15000 15196.3 14 137.2 84 15000 15221.2 15 157.5 90 15000 15247.5 16 179.2 96 15000 15275.2 17 202.3 102 15000 15304.3 18 226.8 108 15000 15334.8 19 252.7 114 15000 15366.7 20 280 120 15000 15400 21 308.7 126 15000 15434.7 22 338.8 132 15000 15470.8 23 370.3 138 15000 15508.3 24 403.2 144 15000 15547.2 25 437.5 150 15000 15587.5 26 473.2 156 15000 15629.2 27 510.3 162 15000 15672.3 28 548.8 168 15000 15716.8 29 588.7 174 15000 15762.7 30 630 180 15000 15810 31 672.7 186 15000 15858.7 32 716.8 192 15000 15908.8 33 762.3 198 15000 15960.3 34 809.2 204 15000 16013.2 35 857.5 210 15000 16067.5 36 907.2 216 15000 16123.2 37 958.3 222 15000 16180.3 38 1010.8 228 15000 16238.8 39 1064.7 234 15000 16298.7 40 1120 240 15000 16360 41 1176.7 246 15000 16422.7 42 1234.8 252 15000 16486.8 43 1294.3 258 15000 16552.3 44 1355.2 264 15000 16619.2 45 1417.5 270 15000 16687.5 46 1481.2 276 15000 16757.2 47 1546.3 282 15000 16828.3 48 1612.8 288 15000 16900.8 49 1680.7 294 15000 16974.7 50 1750 300 15000 17050 51 1820.7 306 15000 17126.7 52 1892.8 312 15000 17204.8 53 1966.3 318 15000 17284.3 54 2041.2 324 15000 17365.2 55 2117.5 330 15000 17447.5 56 2195.2 336 15000 17531.2 57 2274.3 342 15000 17616.3 58 2354.8 348 15000 17702.8 59 2436.7 354 15000 17790.7 60 2520 360 15000 17880 61 2604.7 366 15000 17970.7 62 2690.8 372 15000 18062.8 63 2778.3 378 15000 18156.3 64 2867.2 384 15000 18251.2 65 2957.5 390 15000 18347.5 66 3049.2 396 15000 18445.2 67 3142.3 402 15000 18544.3 68 3236.8 408 15000 18644.8 69 3332.7 414 15000 18746.7 70 3430 420 15000 18850 71 3528.7 426 15000 18954.7 72 3628.8 432 15000 19060.8 73 3730.3 438 15000 19168.3 74 3833.2 444 15000 19277.2

Plutonium 241 has a decay rate of 4.8 % per year. How many years will it take a 50 kg sample to decay to 10 kg? Since 4.8% is 0.048, we have decay as: 50 * (1 - 0.048)^n = 10 0.952^n = 0.2 Typing [URL='https://www.mathcelebrity.com/natlog.php?num=0.952%5En%3D0.2&pl=Calculate']this into our math engine[/URL], we get: n = [B]32.7186 years[/B]

principal $3000, actual interest rate 5.6%, time 3 years. what is the balance after 3 years [URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=3&int=5.6&pl=Annually']Using our compound interest calculator[/URL], we get a final balance of: [B]$3,532.75[/B]

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Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how much will she owe after 4 years? [U]Convert annual amounts to monthly[/U] 4 years = 12 * 4 = 48 months i = .105/12 = 0.00875 monthly [U]Build our accumulation function A(t) where t is the time in months[/U] A(48) = 8,000 * (1.00875)^48 A(48) = 8,000 * 1.5192 A(48) = [B]12,153.60 [/B] [URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=48&int=10.5&pl=Monthly']You can also use the balance calculator[/URL]

Rachel deposits $6000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=6000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get interest paid of [B]$1,440[/B]

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years? The formula for [U]interest[/U] using simple interest is: I = Prt where P = Principal, r = interest, and t = time. We're given P = 500, r =0.04, and t = 4. So we plug this in and get: I = 500(0.04)(4) I = [B]80[/B]

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit? Simple interest formula: A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest. Plugging in our numbers, we get: 400 = P(1 + 0.08(8)) 400 = P(1 + 0.64) 400 = 1.64P 1.64P = 400 [URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get: P = [B]$243.90[/B]

Richard earns $2700 a month. He received a 3% raise. What is Richard's new annual salary? Remember 12 months in 1 year $2,700 per month * 12 months = 32,400 per year. A 3% raise means the new salary is: 32,400 * 1.03 = [B]$33,372[/B]

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages. Let r be Richard's age. And a be Alvin's age. We have: [LIST=1] [*]r = 3a [*]a + r = 52 [/LIST] Substitute (1) into (2) a + 3a = 52 Group like terms: 4a = 52 [URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D52&pl=Solve']Typing this into the search engine[/URL], we get [B]a = 13[/B]. This means Richard is 3(13) = [B]39[/B]

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico? Let Rico's age be r Let Nico's age be n We're given two equations: [LIST=1] [*]r = n + 6 [*]n + r = 36 [/LIST] We plug equation (1) into equation (2) for r: n + n + 6 = 36 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B6%3D36&pl=Solve']type it in our search engine[/URL] and we get: [B]n = 15[/B]

Rochelle deposits $4,000 in an IRA. What will be the value (in dollars) of her investment in 25 years if the investment is earning 8% per year and is compounded continuously? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4000&int=8&t=25&pl=Continuous+Interest']continuous interest calculator[/URL], we get: [B]29,556.22[/B]

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64. Let Sally's age be s. Let Mark's age be m. We're given two equations: [LIST=1] [*]s = m + 4 [*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I] [/LIST] Substitute equation (1) into equation (2): 2(m + 4) + 5m = 64 Multiply through: 2m + 8 + 5m = 64 Group like terms: (2 + 5)m + 8 = 64 7m + 8 = 64 [URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get: m = [B]8[/B]

Sam invested $48,000, some at 6% interest and the rest at 10%. How much did he invest at each rate if he received $4,000 in interest in one year? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=48000&i1=6&i2=10&itot=4000&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*]Fund 1 @ 6% = [B]$20,000[/B] [*]Fund 2 @ 10% = [B]$28,000[/B] [/LIST]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John Let John's age be j. We're given the following equation: 3j - 20 = 52 ([I]Less than[/I] means we subtract) To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get: j = [B]24[/B]

Samantha is y years old now. Represent her age 5 years from now. Represent her age 2 years ago. 5 years from now, Samantha will be [B]y + 5[/B] 2 years ago, Samantha will be [B]y - 2[/B]

Sara earns $6000 more than 1/3 of Claudia's yearly salary. If Claudia's salary is n, what is Sara's salary? 1/3 Claudia's salary: n/3 6000 more means we add: [B]n/3 + 6000[/B]

If a business sells for $1,000,000 (hypothetically)and the proceeds are paid out over 5 years, using the following breakdown: 10% in the first year 15% in the second year 25% in years 3 through 5 Calculate the payouts: [LIST] [*]Year 1: 10% * $1,000,000 = $100,000 [*]Year 2: 15% * $1,000,000 = $150,000 [*]Year 3: 25% * $1,000,000 = $250,000 [*]Year 4: 25% * $1,000,000 = $250,000 [*]Year 5: 25% * $1,000,000 = $250,000 [/LIST] To check our work, add up our proceed payouts: $100,000 + $150,000 + $250,000 + $250,000 + $250,000 = $1,000,000

Sharon is 17 years old. The sum of the ages of Sharon and John is 70. John's age is 70 - Sharon's age. John's age is 70 - 17 = [B]53[/B]

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry? Let Sherry's age be s. Let the mom's age be m. We're given two equations: [LIST=1] [*]s = m - 31 [*]m + s = 61 [/LIST] Substitute equation (1) into equation (2) for s: m + m - 31 = 61 To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm-31%3D61&pl=Solve']we type this equation into our search engine[/URL] and we get: m = 46 Now, we plug m = 46 into equation (1) to find Sherry's age s: s = 46 - 31 s = [B]15[/B]

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. (a) Which of the following is the hypothesis to be conducted? A. H0: p = 0.122, H1 p > 0.122 B. H0: p = 0.122, H1 p <> 0.122 C. H0: p = 0.122, H1 p < 0.122 (b) Which of the following is a Type I error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. c) Which of the following is a Type II error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% (a) [B]C H0: p = 0.122, H1: p < 0.122[/B] because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased. (b) [B]C.[/B] The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true c) [B]C.[/B] The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.

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Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased by approximately 14.3% per year. Write an equation for the number of sports radio stations for t years after 1996. If the trend continues, predict the number of sports radio stations in 2015. Equation - where t is the number of years after 1996: R(t) = 220(1.143)^t We Want R(t) for 2015 t = 2015 - 1996 = 19 R(19) = 220(1.143)^19 R(19) = 220 * 12.672969 [B]R(19) = 2788.05 ~ 2,788[/B]

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in 4 years? [U]Calculate savings amount per month:[/U] Savings amount per month = Earnings - Spend Savings amount per month = 1160 - 540 Savings amount per month = 620 [U]Convert years to months[/U] 4 years = 12 * 4 months 4 years = 48 months [U]Calculate total savings:[/U] Total Savings = Savings per month * number of months saved Total Savings = 620 * 48 Total Savings = [B]$29,760 [MEDIA=youtube]sbzRra8dSFs[/MEDIA][/B]

Sue has $25,000 to invest. She deposits some in stocks and the rest in annuities. If the stocks are at a rate of 6% and the annuities are at a rate of 3% and Sue wants to earn $1200 by the end of the year, find how much Sue deposited into each. Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=25000&i1=6&i2=3&itot=1200&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]15,000 in stocks[/B] [*][B]10,000 in annuities[/B] [/LIST]

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Suppose $10000 is invested in a savings account paying 8% interest per year , after 5 years how much would be in the account compounded continuously Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=10000&int=8&t=5&pl=Continuous+Interest']continuous compounding calculator[/URL], we get 14,918.25

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years Set up the population function P(y) where y is the number of years since now: P(y) = Current population + Growth per year * y Plugging in our numbers at y = 7, we get: P(7) = 740000 + 12620(7) P(7) = 740000 + 88340 P(7) = [B]828,340[/B]

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years. We setup the population function P(y) where y is the number of years of population growth, g is the growth per year, and P(0) is the original population. P(y) = P(0) + gy Plugging in our numbers of y = 7, g = 12,620, and P(0) = 740,000, we have: P(7) = 740,000 + 12,620 * 7 P(7) = 740,000 + 88,340 P(7) = [B]828,340[/B]

Suppose that 25400 is invested in a certificate of a deposit for 3 years at 6% annual interest to be compounded semi annually how much interest will this investment earn? 3 years, compounded semi-annually, gives us 3 x 2 = 6 periods. [URL='https://www.mathcelebrity.com/compoundint.php?bal=25400&nval=6&int=6&pl=Semi-Annually']Using our balance with interest calculator[/URL], we get [B]$30,328.93[/B]

Suppose that you have just purchased a car for $40,000. Historically, the car depreciates by 8% each year, so that next year the car is worth $40000(.92). What will the value of the car be after you have owned it for three years? Book Value B(t) at time t is B(t) = 40,000(1-0.08)^t or B(t) = 40,000(0.92)^t At t = 3 we have: B(3) = 40,000(0.92)^3 B(3) = 40,000 * 0.778688 B(3) = [B]31,147.52[/B]

Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded monthly. Find the account balance after 12 years. Round your answer to two decimal places. Using our[URL='https://www.mathcelebrity.com/compoundint.php?bal=1000&nval=12&int=7.2&pl=Monthly'] compound interest balance calculator[/URL], we get: [B]$1,074.42[/B]

Suppose you deposit $3000 in an account paying 2% annual interest, compounded continuously. Use A=Pert to find the balance after 5 years. A = $3,000 * e^0.02(5) A = $3,000 * e^0.1 A = $3,000 * 1.105171 A = [B]$3,315.51[/B]

Suppose you deposited $1200 in an account paying a compound interest rate of 6.25% quarterly, what would the account balance be after 10 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=1200&nval=40&int=6.25&pl=Quarterly']Using our compound interest with balance calculator[/URL], we get: [B]$2,231.09[/B]

Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1600&int=4.6&t=4&pl=Continuous+Interest']continuous compound calculator[/URL], we get $1,923.23

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3 of the avagrage price at a consignment shop. How much money did she make at the consigment shop? Calculate average price: 1/3 the average price is $30/3 = $10 Total money made: Pairs of Shoes * Average Price 15 * 10 = [B]$150[/B]

The age of a woman 15 years ago Let the woman's current age be a. 15 years ago means we subtract 15 from a: [B]a - 15[/B]

The age of denver 3 years ago if he is x years old now 3 years ago means we subtract: [B]x - 3[/B]

The age of woman 15 years ago Let a be the woman's age today. 15 years ago means we subtract 15 from a: [B]a - 15[/B]

The average age of 15 men is 25 years. What is their total age in years? Average Age = Total Ages/Total Men 25 = Total Ages / 15 Cross multiply and we get: Total Ages = 15 * 25 Total Ages = [B]375[/B]

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. a. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months? b. What is the average precipitation of 5 randomly selected years for the first 7 months? c. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months? [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=1&pl=P%28X+%3E+Z%29']For a. we set up our z-score for[/URL]: P(X>18) = 0.7088 b. We assume the average precipitation of 5 [I]randomly[/I] selected years for the first 7 months is the population mean μ = 19.32 c. [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=5&pl=P%28X+%3E+Z%29']P(X > 18 with n = 5)[/URL] = 0.8907

The buyer of a lot pays P10,000 every month for 10 years. If the money is 8% compounded annually, how much is the cash value of the lot? (use j= 0.006434, n=120) Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=10000&nval=120&int=8&pl=Monthly']compound interest calculator[/URL], we get: [B]22,196.40[/B]

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely? Complete depreciation means the salvage value is 0. So S(t) = 0. We need to find t to make S(t) = 0 -4,500t + 54,000 = 0 Subtract 54,000 from each side -4,500t = -54,000 Divide each side by -4,500 [B]t = 12[/B]

The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students? Set up the Enrollment function E(y) where y is the number of years. [U]High School R:[/U] [I]Increasing[/I] means we add E(y) = 200 + 20y [U]High School T:[/U] [I]Decreasing[/I] means we subtract E(y) = 400 - 30y When the two schools have the same enrollment, we set the E(y) functions equal to each other 200 + 20y = 400 - 30y To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=200%2B20y%3D400-30y&pl=Solve']type it in our search engine[/URL] and we get: y = [B]4[/B]

The famous mathematician Pythagoras founded the Mathematical Brotherhood in 530 BC. About how many years ago did this happen? BC means before year 0. So we take the current year, which at the time of this post, is 2021. We [U]add[/U] 530 years to that since BC is before year 0, and we get: 2021 + 530 = [B]2551 years ago[/B]

the initial deposit in a bank account was $6000 and it has an annual interest rate of 4.5%. Find the amount of money in the bank after 3 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6000&nval=4.5&int=3&pl=Annually']balance and interest calculator[/URL], we get: [B]$6,853.60[/B]

The jimenez family inherited land that was purchased for $50,000 in 1967. The value of the land increased by approximately 4% per year. What is the approximate value of the land by the year 2016? 1967 to 2016 is 49 years. So we have 341,667.47 using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=50000&int=4&t=49&pl=Compound+Interest']compound interest calculator[/URL].

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office? Mean is another word for [U]average[/U]. Mean age of women = Sum of all ages women / number of women We're told mean age of women is 30, so we have: Sum of all ages women / 10 = 30 Cross multiply, and we get: Sum of all ages of women = 30 * 10 Sum of all ages of women = 300 Mean age of men = Sum of all ages men / number of men We're told mean age of men is 29, so we have: Sum of all ages men / 10 = 29 Cross multiply, and we get: Sum of all ages of men = 29 * 10 Sum of all ages of men = 290 [U]Calculate mean age (nearest year) of all the people in the office:[/U] mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office mean age of all the people in the office = (300 + 290) / (10 + 10) mean age of all the people in the office = 590 / 20 mean age of all the people in the office = 29.5 The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30. Because the decimal is greater or equal to 0.5 (halfway), we round [U]up[/U] to [B]30[/B]

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. What is the age of the person who entered the room? The sum of the 5 people's scores is S. We know: S/5 = 28 Cross multiply: S = 140 We're told that: (140 + a)/6 = 32 Cross multiply: 140 + a = 192 [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D192&pl=Solve']Type this equation into our search engine[/URL], we get: a = [B]52[/B]

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room? Mean = Sum of Ages in Years / Number of People 32 = Sum of Ages in Years / 5 Cross multiply: Sum of Ages in Years = 32 * 5 Sum of Ages in Years = 160 Calculate new mean after the next person enters the room. New Mean = (Sum of Ages in Years + New person's age) / (5 + 1) Given a new Mean of 40, we have: 40 = (160 + New person's age) / 6 Cross multiply: New Person's Age + 160 = 40 * 6 New Person's Age + 160 = 240 Let the new person's age be n. We have: n + 160 = 240 To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get: n = [B]80[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room? The mean formulas is denoted as: Mean = Sum of Ages / Total People We're given Mean = 38 and Total People = 5, so we plug in our numbers: 28 = Sum of Ages / 5 Cross multiply, and we get: Sum of Ages = 28 * 5 Sum of Ages = 140 One more person enters the room. The mean age is now 39. Set up our Mean formula: Mean = Sum of Ages / Total People With a new Mean of 39 and (5 + 1) = 6 people, we have: 39 = Sum of Ages / 6 But the new sum of Ages is the old sum of ages for 5 people plus the new age (a): Sum of Ages = 140 + a So we have: 29 = (140 + a)/6 Cross multiply: 140 + a = 29 * 6 140 + a = 174 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get: a = [B]34[/B]

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement? Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality: 6a >= 50 To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get: [B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

The monthly rental for an apartment is $412.50. How much would the rent be for one year? Since there are 12 months in a year, we have: Yearly Rent = Monthly Rent * 12 Yearly Rent = $412.50 * 12 Yearly Rent = [B]$4,950[/B]

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what was the population in 1981? Calculate the difference in years: Difference = 1981 - 1945 Difference = 36 Calculate doubling periods: Doubling periods = Total years / Doubling time Doubling periods = 36/12 Doubling periods = 3 Population = Initial Population * 2^doubling periods Population = 11005 * 2^3 Population = 11005 * 8 Population = [B]88,040[/B]

The population of a town is currently 22,000. This represents an increase of 40% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole number if necessary. To get the population 5 years ago, we'd discount the current population of 22,000 by 40%. We can write a 40% discount as 1.4. Population 5 years ago = 22,000/1.4 Population 5 years ago = 15,714.29 Rounding to the nearest whole number, we get [B]15,714[/B]

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present? [U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U] p(0) = 4000 - 3000e^-0.2(0) p(0) = 4000 - 3000e^0 p(0) = 4000 - 3000(1) p(0) = 4000 - 3000 [B]p(0) = 1000[/B]

The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per year since. Write an expression that shows the population of Westport at the beginning of 1994 and solve. 1994 - 1980 = 14 years. Using our [URL='https://www.mathcelebrity.com/population-growth-calculator.php?num=thepopulationofwestportwas43000hassteadilydecreasedby1%for14years&pl=Calculate']population calculator[/URL], we get: [B]37,356[/B]

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk [I]m[/I] and cups of juice [I]j[/I] a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? Total calcium = Milk calcium + Juice Calcium Calculate Milk Calcium: Milk Calcium = 299m where m is the number of cups of milk Calculate Juice Calcium: Juice Calcium = 261j where j is the number of cups of juice The phrase [I]meet or exceed[/I] means greater than or equal to, so we have an inequality, where Total Calcium is greater than or equal to 1000. So we write our inequality as: Milk calcium + Juice Calcium >= Total Calcium [B]299m + 261j >= 1000[/B]

The rent for an apartment is $6600 per year and increases at a rate of 4% each year. Find the rent of the apartment after 5 years. Round your answer to the nearest penny. Our Rent R(y) where y is the number of years since now is: R(y) = 6600 * (1.04)^y <-- Since 4% is 0.04 The problem asks for R(5): R(5) = 6600 * (1.04)^5 R(5) = 6600 * 1.2166529024 R(5) = [B]8,029.91[/B]

The school council began the year with a $600 credit to their account, but they spent $2,000 on new books for classrooms. How much must the PTA earn through fundraising to break even? +600 - 2000 = -1,400. Break even means no profit or loss. So the PTA must earn [B]1,400 [/B]to break even on the -1,400

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point. [U]Calculate cost function C(b) with b as the number of books:[/U] C(b) = Cost per book * b + Overhead [B]C(b) = 15b + 5500[/B] [U]Calculate Revenue Function R(b) with b as the number of books:[/U] R(b) = Sales Price per book * b [B]R(b) = 40b[/B] [U]Calculate break even function E(b):[/U] Break-even Point = Revenue - Cost Break-even Point = R(b) - C(b) Break-even Point = 40b - 15b - 5500 Break-even Point = 25b - 5500 [U]Calculate break even point:[/U] Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0 25b - 5500 = 0 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: [B]b = 220[/B]

The set of months of a year ending with the letters “ber”. We build set S below: [B]S = {September, October, November, December}[/B] The cardinality of S, denoted |S|, is the number of items in S: [B]|S| = 4[/B]

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now? Let Jocelyn's age be a Let Joseph's age be b. We're given two equations: [LIST=1] [*]a + b = 40 [*]2(a + 5) = b + 5 [/LIST] We rearrange equation (1) in terms of a to get: [LIST=1] [*]a = 40 - b [*]2a = b + 5 [/LIST] Substitute equation (1) into equation (2) for a: 2(40 - b) = b + 5 80 - 2b = b + 5 To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=80-2b%3Db%2B5&pl=Solve']type it in our search engine[/URL] and we get: [B]b (Joseph's age) = 25[/B] Now, substitute b = 25 into equation (1) to solve for a: a = 40 - 25 [B]a (Jocelyn's age) = 15[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: [LIST=1] [*]l + r = 89 [*]l - 7 = 4(r - 7) [/LIST] Simplify equation 2 by multiplying through: [LIST=1] [*]l + r = 89 [*]l - 7 = 4r - 28 [/LIST] Rearrange equation 1 to solve for r and isolate l by subtracting l from each side: [LIST=1] [*]r = 89 - l [*]l - 7 = 4r - 28 [/LIST] Now substitute equation (1) into equation (2): l - 7 = 4(89 - l) - 28 l - 7 = 356 - 4l - 28 l - 7 = 328 - 4l To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get: l = [B]67[/B]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins? Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given: [LIST=1] [*]a + h + c = 48 [*]a = 0.5h [*]a = c + 4 [/LIST] To isolate equations in terms of Suresh's age (a), let's do the following: [LIST] [*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4 [*]Rewriting (2) by multiply each side by 2, we have h = 2a [/LIST] We have a new system of equations: [LIST=1] [*]a + h + c = 48 [*]h = 2a [*]c = a - 4 [/LIST] Plug (2) and (3) into (1) a + (2a) + (a - 4) = 48 Group like terms: (1 + 2 + 1)a - 4 = 48 4a - 4 = 48 [URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 13 [/B]<-- Suresh's age This means that Hakima's age, from modified equation (2) above is: h = 2(13) [B]h = 26[/B] <-- Hakima's age This means that Saad's age, from modified equation (3) above is: c = 13 - 4 [B]c = 9[/B] <-- Saad's age [B] [/B]

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 26% each year, what is the exponential formula Let y be the number of years since 1990. We have the formula T(y): [B]T(y) = 951 * 1.26^y[/B]

The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much the van will be worth in 7 years. Each year, the van is worth 100% - 4% = 96%, or 0.96. We have the Book value equation: B(t) = 15000(0.96)^t where t is the time in years from now. The problem asks for B(7): B(7) = 15000(0.96)^7 B(7) = 15000(0.7514474781) B(7) = [B]11,271.71[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds. If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line? Change times to seconds: [LIST] [*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds [*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds [/LIST] Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line. 1 mile = 5280 feet: Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled 5280/276.5 = n/223.13 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: n = 4260.85 feet Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

Theodore invests $17,000 at 9% simple interest for 1 year. How much is in the account at the end of the 1 year period. Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=17000&int=9&t=1&pl=Simple+Interest']balance calculator with simple interest[/URL], we have: [B]18,530[/B]

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will be 312,500 graphic designer jobs in 2020. (a) Using the data, find the number of graphic designer jobs as a linear function of the year. [B][U]Figure out the linear change from 2010 to 2020[/U][/B] Number of years = 2020 - 2010 Number of years = 10 [B][U]Figure out the number of graphic designer job increases:[/U][/B] Number of graphic designer job increases = 312,500 - 286,200 Number of graphic designer job increases = 26,300 [B][U]Figure out the number of graphic designer jobs added per year[/U][/B] Graphic designer jobs added per year = Total Number of Graphic Designer jobs added / Number of Years Graphic designer jobs added per year = 26,300 / 10 Graphic designer jobs added per year = 2,630 [U][B]Build the linear function for graphic designer jobs G(y) where y is the year:[/B][/U] G(y) = 286,200 + 2,630(y - 2010) [B][U]Multiply through and simplify:[/U][/B] G(y) = 286,200 + 2,630(y - 2010) G(y) = 286,200 + 2,630y - 5,286,300 [B]G(y) = 2,630y - 5,000,100[/B]

Tiffany is 59 years old. The sum of the ages of Tiffany and Maria is 91. How old is Maria? Tiffany + Maria = 91 59 + Maria = 91 Subtract 59 from each side Maria = 91 - 59 [B]Maria = 32[/B]

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Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what is the value of the car expected to be 6 years from now. Depreciation at 8% per year means it retains (100% - 8%) = 92% of it's value. We set up our depreciation function D(t), where t is the number of years from right now. D(t) = $42,000(0.92)^t The problem asks for D(6): D(6) = $42,000(0.92)^6 D(6) = $42,000(0.606355) D(6) = [B]$25,466.91[/B]

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be? Let my current age be a. We're given: 4/5a > 3/4(a + 1) Multiply through on the right side: 4a/5 > 3a/4 + 3/4 Let's remove fractions by multiply through by 5: 5(4a/5) > 5(3a/4) + 5(3/4) 4a > 15a/4 + 15/4 Now let's remove the other fractions by multiply through by 4: 4(4a) > 4(15a/4) + 4(15/4) 16a > 15a + 15 [URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get: a > 15 This means the smallest [I]integer age[/I] which the problem asks for is: 15 + 1 = [B]16[/B]

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill? Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations: [LIST=1] [*]t = s + 2 [*]b = 2t [*]s + t + b - 2 = 20 [/LIST] Get (2) in terms of s (2) b = 2(s + 2) <-- using (1), substitute for t So we have (3) rewritten with substitution as: s + (s + 2) + 2(s + 2) - 2 = 20 s + (s + 2) + 2s + 4 - 2 = 20 Group like terms: (s + s + 2s) + (2 + 4 - 2) = 20 4s + 4 = 20 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B4%3D20&pl=Solve']equation calculator [/URL]to get s = 4 Above, we had b = 2(s + 2) Substituting s = 4, we get: 2(4 + 2) = 2(6) = [B]12 Bill is 12 years old[/B]

Two years of local internet service costs 685, including the installation fee of 85. What is the monthly fee? Subtract the installation fee of 85 from the total cost of 685 to get the service cost only: 685 - 85 = 600 Now, divide that by 24 months in 2 years to get a per month fee 600/24 = [B]25 per month[/B]

Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food a.) write an equation that relates the amount in the account (a) with the number of (w) weeks b.) How many weeks will it take until Tyler runs out of money? [U]Part a) where w is the number of weeks[/U] a = Initial account value - weekly spend * w ([I]we subtract because Tyler spends)[/I] a = [B]1200 - 21w [/B] [U]Part b)[/U] We want to know the number of weeks it takes where a = 0. So we have: 1200 - 21w = 0 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-21w%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: w = 57.14 weeks The problem asks for when he runs out of money, so we round up to [B]58 whole weeks[/B]

Vacation is 72 days long. What percent of the entire year is summer vacation ? Vacation day Percent = 100% * Vacation Days / Total Days in the year Vacation day Percent = 100% * 72/365 Vacation day Percent = 100% * [URL='https://www.mathcelebrity.com/perc.php?num=72&den=365&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']0.1973[/URL] Vacation day Percent = [B]19.73%[/B]

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years. Let Victoria's age be v. And her neighbor's age be n. We're given: [LIST=1] [*]v = n + 4 [*]v + n <=14 <-- no more than means less than or equal to [/LIST] Substitute Equation (1) into Inequality (2): (n + 4) + n <= 14 Combine like terms: 2n + 4 <= 14 [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get: n <= 5 Substituting this into inequality (2): v + 5 <= 14 [URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get: [B]v <= 9[/B]

Warren was making $100,000 per year. His boss said that he was going to cut his salary 25%, but that Warren shouldn't worry because he would be given a 25% raise the next day. How much will Warren's salary be after the 25% cut and 25% raise? Cut salary: 100,000 * 0.75 = 75,000 New salary after raise: 75,000 * 1.25 = [B]93,750[/B]

What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round to three decimal places. Use a 365 day year. [U]Set up the accumulation equation:[/U] (1+i)^365 = 1.054 [U]Take the natural log of each side[/U] 365 * Ln(1 + i) = 1.054 Ln(1 + i) = 0.000144089 [U]Use each side as a exponent to eulers constant e[/U] (1 + i) = e^0.000144089 1 + i = 1.000144099 i = 0.000144099 or [B].0144099%[/B]

What is the simple interest accrued from a $500 investment at 7% interest for 5 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=500&int=7&t=5&pl=Simple+Interest']simple interest balance calculator[/URL], we get $175 in simple interest earned.

When an alligator is born it is about 8 inches long each year they grow 12 inches determine the age and years of 116 inch alligator? Calculate inches to grow to get to 116 116 - 8 = 108 Now figure out how many years it takes growing at 12 inches per year, using y as years 12y = 108 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=12y%3D108&pl=Solve']equation calculator[/URL], we get: [B]y = 9[/B]

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck every other week, how much does Winnie receive from each paycheck? Subtract the taxes to get Winnie's Total net pay: Total Net Pay = Annual Salary - Annual Taxes Total Net Pay =$55,117 - $3,715 Total Net Pay = $51,402 Now, if Winnie gets paid every other week, and there are 52 weeks in a year, then she gets paid 26 times. Calculate single paycheck amount Single Paycheck Amount = Total Net Pay / 26 payments Single Paycheck Amount = $51,402 / 26 Single Paycheck Amount = [B]$1,977[/B]

Suppose the consumption of electricity grows at 5.3% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round to the nearest hundredth.

A man is three times as old as his son was at the time when the father was twice as old as his son will ne two years from now. Find the present ages of each person.

You are given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2% or the interest on $100,000 invested for 5 years at an interest rate of 2% compounded daily. Which investment earns the greater amount of interest? Give the difference between the amounts of interest earned by the two investments [URL='http://www.mathcelebrity.com/simpint.php?av=&p=100000&int=2&t=5&pl=Simple+Interest']Simple interest balance after 5 years[/URL] at 2% is $110,000. [URL='http://www.mathcelebrity.com/compoundint.php?bal=100000&nval=1825&int=2&pl=Daily']Daily compounded interest for 5 years[/URL] at 2% is 365 days per year * 5 years = 1,825 days = [B]$110,516.79 Compound interest earns more by $110,516.79 - $110,000 = $516.79[/B]

You buy a house for $130,000. It appreciates 6% per year. How much is it worth in 10 years The accumulated value in n years for the house is: A(n) = 130,000(1.06)^n We want A(10) A(10) = 130,000(1.06)^10 A(10) =130,000*1.79084769654 A(10) = [B]232,810.20[/B]

You deposit $150 into an account that yields 2% interest compounded quarterly. How much money will you have after 5 years? 2% per year compounded quarterly equals 2/4 = 0.5% per quarter. 5 years * 4 quarter per year = 20 quarters of compounding. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=150&nval=20&int=2&pl=Quarterly']balance calculator[/URL], we get [B]$165.73[/B] in the account after 20 years.

You deposit $1600 in a bank account. Find the balance after 3 years if the account pays 1.75% annual interest compounded monthly Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=1600&nval=36&int=1.75&pl=Monthly']compound interest calculator with 3 years = 36 months[/URL], we get: [B]1,686.18[/B]

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest? The simple interest formula for the accumulated balance is: Prt = I We are given P = 2,000, r = 0.04, and I = 500. 2000(0.04)t = 500 80t = 500 Divide each side by 80 t = [B]6.25 years [MEDIA=youtube]Myz0FZgwZpk[/MEDIA][/B]

you deposit $2000 in an account that pays 3% annual interest. Find the balance after 10 years if the interest is compounded quarterly. Please give your answer to 2 decimal places. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2000&nval=40&int=3&pl=Quarterly']compound interest calculator, with 10 * 4 = 40 quarters[/URL], we have: [B]$2,696.70[/B]

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years. The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is: A = B(1 + i)^n [U]Givens[/U] [LIST] [*]4 years of quarters = 4 * 4 = 16 quarters. So this is t. [*]Interest per quarter = 5/4 = 1.25% [*]Initial Balance (B) = 750. [/LIST] Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=16&int=5&pl=Quarterly']compound balance interest calculator[/URL], we get the accumulated value A: [B]$914.92[/B]

You deposit $8500 in an account that pays 1.78% annual interest. Find the balance after 10 years when the interest is compounded monthly. 10 years * 12 months per year = 120 months. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=8500&nval=120&int=1.781&pl=Monthly']compound interest calculator[/URL], we get a balance of: [B]$10,155.69[/B]

You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1300&nval=10&int=5&pl=Annually']compound interest balance calculator[/URL], we get: [B]$2,117.56[/B]

You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value of the car after 7 years. Round your answer to the nearest cent. Set up the Depreciation equation: D(t) = 23,000/(1.15)^t We want D(7) D(7) = 23,000/(1.15)^7 D(7) = 23,000/2.66002 D(7) = [B]8,646.55[/B]

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If the rate of decrease continues, what is the value of your car in 5 years? Set up the depreciation function D(t), where t is the time in years from purchase. We have: D(t) = 35,000(1 - 0.085)^t Simplified, a decrease of 8.5% means it retains 91.5% of it's value each year, so we have: D(t) = 35,000(0.915)^t The problem asks for D(5) D(5) = 35,000(0.915)^5 D(5) = 35,000(0.64136531607) D(5) = $[B]22,447.79[/B]

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in 23 years? Build the accumulation of principal. We multiply 5,500 times 1.048 raised to the 23rd power. Future Value = 5,500 (1.048)^23 Future Value =5,500(2.93974392046) Future Value = 16,168.59 The question asks for interest earned, so we find this below: Interest Earned = Future Value - Principal Interest Earned = 16,168.59 - 5,500 Interest Earned = [B]10,668.59[/B]

you save $35 a week for a year. How much do you have at the end of the year? We know that 1 year = 52 weeks $35 per week * 52 weeks = [B]$1,820 saved for the year[/B]

You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays 4% annual interest. After one year, you have earned a total of $69.50 in interest. How much money did you invest in each account. Explain. Let a be the amount you invest in Account A. So this means you invested 1500 - A in account B. We have the following equation: 05a + (1500 - a).04 = 69.50 Simplifying, we get: 0.05a + 1560 - 0.04a = 69.50 0.01a + 60 = 69.50 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.01a%2B60%3D69.50&pl=Solve']equation solver[/URL], we get: [B]a = 950[/B] So this means Account B is b = 1500 - 950 = [B]550[/B]

you start with 150$ in year bank account if you save $28 a year with equation would model your savings find equation. We create a savings function S(y) where y is the number of years since the start. S(y) = Savings per year * y + initial savings [B]S(y) = 28y + 150[/B]

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months. Set up a savings function for m months [B]S(m) = 491 + 11m[/B]

Your friend deposits 9500$ in an investment account that earns 2.1% annual interest find the balance after 11 years when the interest is compounded quarterly 11 years * 4 quarters per year = 44 quarters Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=9500&nval=44&int=2.1&pl=Quarterly']compound interest with balance calculator[/URL], we have: [B]11,961.43[/B]

Your grandfather gave you $12,000 a a graduation present. You decided to do the responsible thing and invest it. Your bank has a interest rate of 6.5%. How much money will you have after 10 years if the interest is compounded monthly? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=12000&nval=120&int=6.5&pl=Monthly']compound interest calculator[/URL], we have 10 years * 12 months = 120 months. [B]$22,946.21[/B]

Your grandma gives you $10,000 to invest for college. You get an average interest rate of 5% each year. How much money will you have in 5 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=10000&nval=5&int=5&pl=Annually']accumulated balance calculator[/URL], we get: [B]12,762.82[/B]

your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it take you to make $80000? Let y be the number of years of compounding the 2% raise. Since 2% as a decimal is 0.02, we have the following equation for compounding the salary: 45000 * (1.02)^y = 80000 Divide each side by 45000: (1.02)^y = 1.77777777778 To solve this equation for y, we [URL='https://www.mathcelebrity.com/natlog.php?num=1.02%5Ey%3D1.77777777778&pl=Calculate']type it in our search engine[/URL] and we get: y = [B]29.05[/B] [B]Or just over 29 years[/B]

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