Using the Rule of 72...
How long for money to double at 19%?
Doubling Time Definition:
(1 + i)n = 2
1 unit of money doubles inn 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 = 19%
| n = | 0.6931 * 0.19 |
| 0.19 * Ln(1 + 0.19) |
| n = | 0.6931 * 0.19 |
| 0.19 * Ln(1.19) |
Now simplify the 2nd term
| n = | 0.6931 * 0.19 |
| i * 0.17395330712344 |
| n = | 0.6931 * 1.092247127358 |
| i |
| n~ = | 0.72 |
| i |
Substitute i = 0.19 into the quotient
| n~ = | 0.72 |
| 0.19 |
n = 3.7894736842105This means at an interest rate of 19%, we double our money approximately every 3.7894736842105 periods of time.
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What is the Answer?
n = 3.7894736842105
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.
What 3 formulas are used for the Rule of 72 Calculator?
Doubling Money Time (t) = 0.72/i(1 + i)t = 2
For more math formulas, check out our Formula Dossier
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 interestA = (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
Example calculations for the Rule of 72 Calculator
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