The Rule of 72 reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Rule of 72

In finance, the Rule of 72 is a simple method of calculating the approximate number of periods over which a quantity will double. If you divide 72 by the expected growth rate, expressed as a percentage, the answer is approximately the number of periods to double the original quantity. For instance, if you were to invest $100 at 9% per annum, then your investment would be worth $200 after 8.0432 years, using an exact calculation. The rule of 72 gives 72/9=8 years, which is close to the exact answer.

On the other hand if you were to leave $100 uninvested when inflation was 9% per annum, the purchasing power of your $100 would have halved after 8 (72/9) years.

Derivation

So for very small rates, 69.3 would be more accurate than 72. For higher rates, a bigger numerator would be better (e.g. for 20%, using 76 to get 3.8 years would be more accurate than 3.6). 72 is reasonable approximation across this range and is easily divisible by many numbers.

See also: exponential growth, Taylor series

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