Rule of 72

In finance, the rule of 72, the rule of 71, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time or halving time. These rules apply to exponential growth and decay respectively, and are therefore used for compound interest as opposed to simple interest calculations.

To estimate the number of periods required to double an original investment, divide the most convenient "rule-quantity" by the expected growth rate, expressed as a percentage.

For instance, if you were to invest $100 with compounding interest at a rate of 6% per annum, the rule of 72 gives 72/6 = 12 years required for the investment to be worth $200; an exact calculation gives 11.896 years.

Similarly, to determine the time it takes for the value of money to half at a given rate, divide the rule quantity by that rate.

To determine the time for money's buying power to halve, financiers simply divide the rule-quantity by the inflation rate. Thus at 3.5% inflation using the rule of 70, it should take approximately 70/3.5 = 20 years for the value of a unit of currency to halve.

The value 72 is a convenient choice of numerator, since it has many small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. However, depending on the rate and compounding period in question, other values will provide a more appropriate choice. The rule of 72 provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%). The approximations are less accurate at higher interest rates.