Rule of 72

Compounding is the process of finding an unknown future value from a known present value—that is, moving forward in time from a known amount in the present to an unknown amount at some point in the future. Obviously, in dollar terms, future values are larger amounts than are present values because of the time value of money (INTEREST RATES are always positive, never negative). An ever-popular compounding question is, “How long will it take for my money to double?” or “How long will it take for the account to double?” The rule of 72 estimates with a surprising degree of precision how long it will take for a sum to double at some given rate of interest, compounded annually. The number 72 is the numerator, and the denominator is the rate of interest applicable to the situation in question. For example, at 10-percent interest compounded annually, it will take approximately 72/10 = 7.2 years for a sum to double. At 7-percent interest compounded annually, it will take approximately 72/7 = 10 years to double. The rule of 115, also a compounding technique, will approximate how long it takes for a sum to triple at some given rate of interest, compounded annually. The number 115 is the numerator, and the denominator is the rate of interest applicable to the situation in question. For example, at 10-percent interest compounded annually, it takes approximately 115/10 = 11.5 years for a sum to triple. While these two rules are fast and easy to use, more accurate results are obtained by using an interest table of future-value interest factors. However, the published interest factor tables carrying the interest factors to only four places to the right of the decimal. The interest factors are therefore rounded off to four decimal places. The most accurate results are obtained by using a financial calculator.
See also COMPOUNDING, FUTURE VALUE.