rule of 72

Rule of 72

A formula used to determine the amount of time it will take for invested money to double at a given compound interest rate, which is 72 divided by the interest rate. The logic is as follows. The time for an amount A to double is given by 2A=A(1+i)^t where ^ represents exponent and i is the interest rate, e.g. .05 is 5%. The A term cancels from both sides of the question. Solve for t by taking the natural log of both sides of the equation. Hence, t= [ln(2) over {ln(1+i)}], which is approximately equal to 0.72 over i. Hence the rule of 72.

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rule of 72

The mathematical rule used in approximating the number of years it will take a given investment to double in value. The number of years to double an investment is calculated by dividing 72 by the annual rate of return. Thus, an investment expected to earn 10% annually will double the investor's funds in ⁷²/₁₀ , or 7.2 years. Dividing 72 by the number of years in which the investor wishes to double his or her funds will yield the necessary rate of return.