The Rule of 72 is a rule of thumb that states that the number of time periods (such as years) that it takes for a sum to double at compound interest is very nearly 72 divided by the percentage interest rate per period. Thus, for example, it takes (almost exactly) 9 years for a sum to double at 8% interest compounded yearly.
1. Using the rule, find the annual rate of increase for an investment that has quadrupled in 24 years. Compare to the exact value.
2. At what interest rate is the rule exact?
3. Justify the rule using mathematical analysis and a few numerical calculations.
1) Using the rule: Since the investment must double in 12 years in order to quadruple in 24, the rule gives 72/12 = 6 percent interest. The exact value can be found from (1+r)^12 = 2, or 12*log(1+r) = log(2), so that r=.059463, or 5.9463%.
Puzzle Answer
