Using the Rule of 72...
How long for money to double at 7%?
Doubling Time Definition:
(1 + i)n = 2
1 unit of money doubles in
n periods at interest rate i is:
(1 + i)n = 2
Take the natural log of both sides:
Ln(1 + i)n = Ln(2)
Use a logarithmic identity
Ln(an) = n * Ln(a)
Using that identity, we have a = (1 + i):
n * Ln(1 + i) = Ln(2)
Divide both sides by Ln(1 + i)
| n = | Ln(2) |
| Ln(1 + i) |
| n = | 0.6931 |
| Ln(1 + i) |
Multiply the top and bottom by i
| n = | 0.6931 * i |
| Ln(1 + i) * i |
Plug in our interest rate of i = 7%
| n = | 0.6931 * 0.07 |
| 0.07 * Ln(1 + 0.07) |
| n = | 0.6931 * 0.07 |
| 0.07 * Ln(1.07) |
Now simplify the 2nd term
| n = | 0.6931 * 0.07 |
| i * 0.067658648473815 |
| n = | 0.6931 * 1.034605354659 |
| i |
| n~ = | 0.72 |
| i |
Substitute i = 0.07 into the quotient
| n~ = | 0.72 |
| 0.07 |
n = 10.285714285714
This means at an interest rate of 7%, we double our money approximately every 10.285714285714 periods of time.
This means at an interest rate of 7%, we double our money approximately every 10.285714285714 periods of time.
Test Your Knowledge?
- The Rule of 72 is a way to estimate the ___ time?
- The Rule of 72 fraction uses interest rate as the denominator and what value as the numerator?
What is the Answer?
n = 10.285714285714
How does the Rule of 72 Calculator work?
Free Rule of 72 Calculator - Calculates how long it would take money to double (doubling time) using the rule of 72 interest approximation as well as showing the mathematical proof of the Rule of 72.
This calculator has 1 input.
This calculator has 1 input.
What 3 formulas are used for the Rule of 72 Calculator?
Doubling Money Time (t) = 0.72/i
(1 + i)t = 2
(1 + i)t = 2
What 6 concepts are covered in the Rule of 72 Calculator?
- approximation
- anything that is intentionally similar but not exactly equal to something else.
- compound interest
- the interest you earn on principal and interest
A = (1 + r/n)nt - interest rate
- the proportion of a loan that is charged as interest to the borrower or proportion of principal credit given to a depositor
- logarithm
- the exponent or power to which a base must be raised to yield a given number
- rule of 72
- a simplified formula that calculates how long it will take for an investment to double in value, based on its rate of return.
t ~ 72/i - yield
- How much an investment returns in terms of interest rate
