A useful rule of thumb for the time it takes an investment to double with discrete compounding is the “Rule of 72.” To use the Rule of 72, you divide 72 by the rate to determine the number of periods it takes for a value today to double. For example, if the rate is 6 percent, the Rule of 72 says it will take 72/6 = 12 years to double. This is approximately equal to the actual answer of 11.90 years. The Rule of 72 also can be applied to determine what rate is needed to double money in a specified period.

This is a useful approximation for many rates and periods. At what rate is the Rule of 72 exact?