Rule 72

n 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.

The Eckart-McHale Rule (the E-M Rule) provides a multiplicative correction to these approximate results, while Felix's Corollary provides a method of estimating the future value of an annuity using the same principles.

Using the rule to estimate compounding periods

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 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to be worth $200; an exact calculation gives 8.0432 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.

# To estimate the impact of additional fees on financial policies (eg. mutual fund fees and expenses, loading and expense charges on variable universal life insurance investment portfolios), divide 72 by the fee. For example, if the Universal Life policy charges a 3% fee over and above the cost of the underlying investment fund, then the total account value will be cut to 1/2 in 72 / 3 = 24 years, and then to just 1/4 the value in 48 years, compared to holding the exact same investment outside the policy.