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.

(In reply to re: Continuous compounding case by John)

Continuous compounding is the formula you gave as the number of periods increases without bound.  (The limit as number of periods approaches infinity.)

In the formula:
P = principal
e = the constant e
r = rate as a decimal
t = time in years

 

Posted by Jer on 2005-01-25 18:53:51