For an Annuity Immediate:
Payment = 1
n = 5
Interest Rate = 10
Calculate Present Value, Accumulated Value
PV annuity immediate formula:
| an|i = | Payment * (1 - vn) |
| i |
Calculate v:
| v = | 1 |
| 1 + i |
| v = | 1 |
| 1 + 0.1 |
| v = | 1 |
| 1.1 |
v = 0.90909090909091
Calculate PV given i = 0.1, n = 5, and v = 0.90909090909091
| a5|0.1 = | 1 * (1 - 0.909090909090915) |
| 0.1 |
| a5|0.1 = | 1 * (1 - 0.62092132305916) |
| 0.1 |
| a5|0.1 = | 1 * 0.37907867694084 |
| 0.1 |
| a5|0.1 = | 0.37907867694084 |
| 0.1 |
a5|0.1 = 3.7908
AV annuity immediate formula:
| sn|i = | Payment * ((1 + i)n - 1) |
| i |
Calculate AV given i = 0.1, n = 5
| s5|0.1 = | 1 * ((1 + 0.1)5 - 1) |
| 0.1 |
| s5|0.1 = | 1 * (1.15 - 1) |
| 0.1 |
| s5|0.1 = | 1 * (1.61051 - 1) |
| 0.1 |
| s5|0.1 = | 1 * 0.61051 |
| 0.1 |
| s5|0.1 = | 0.61051 |
| 0.1 |
s5|0.1 = 6.1051
How much of AV is principal?:
Principal = Payment Amount * nPrincipal = 1 * 5
Principal = 5
Calculate Interest Paid:
Interest Paid = Accumulated Value - PrincipalInterest Paid = 6.1051 - 5
Interest Paid = 1.11
What is the Answer?
Interest Paid = 1.11
How does the Annuities Calculator work?
Free Annuities Calculator - Solves for Present Value, Accumulated Value (Future Value or Savings), Payment, or N of an Annuity Immediate or Annuity Due.
This calculator has 5 inputs.
This calculator has 5 inputs.
What 4 formulas are used for the Annuities Calculator?
PV Annuity Immediate = Pmt * (1 - vn)/i
PV Annuity Immediate = Pmt * (1 - vn)/d
Accumulated Value of Annuity Immediate = Pmt * ((1 + i)n - 1)/i
Accumulated Value of Annuity Immediate = Pmt * ((1 + i)n - 1)/d
PV Annuity Immediate = Pmt * (1 - vn)/d
Accumulated Value of Annuity Immediate = Pmt * ((1 + i)n - 1)/i
Accumulated Value of Annuity Immediate = Pmt * ((1 + i)n - 1)/d
What 8 concepts are covered in the Annuities Calculator?
- accumulated value
- The total value of an investment, including principal and interest accrued
- annuities
- annuity
- A stream of payments
- future value
- the value of a current asset at a future date based on an assumed rate of growth
- interest
- payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate
- interest rate
- the proportion of a loan that is charged as interest to the borrower or proportion of principal credit given to a depositor
- present value
- the value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.
PV = FV/(1 + i)n
where I is the interest rate per period, PV = Present Value, and FV = Future Value - principal
- The amount borrowed on a loan, before interest is charged
