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 Continuous compounding case by Jer)

I have the formula as:

Principal * (1+periodic growth rate%)^(number of periods) = FinalValue

Not sure what your formula's variables represent.  I concur with your calculations to answer questions 1 and 2.  As far as #3 goes, I can't justify the rule of 72 because it is an approximation which is only coincidentally accurate as you approach the 8-period mark, and increasingly inaccurate beyond that.  The only justification I can come up with is that it saves some financial advisors from having to calculate projections forward using something more complicated than a basic calculator.

Posted by John on 2005-01-25 18:37:39