The Rule of 72

What is this "Rule of 72", that you run across in investing sooner or later (or right now as you read this)?

It is a fast, simple and reasonably accurate way to estimate how fast your money doubles.

Common Use 1: If your money grows by a consistent G% every year, then it will double after 72/G years.
Example 1: your savings account offers 4% a year. After (72/4) = 18 years, your money will have doubled.

Example 2: Yale's endowment under David Swensen grew at a truly remarkable16.1% a year for many, many years. The endowment was doubling in value every (72/16.1) = 4.47 ~ 4.5 years (!).

Being an approximation, the rule of 72 can't be used indiscriminately, but it is useful for typical investment returns.

• It is very accurate for G% between 5% to 12%
• It is reasonably accurate for G% between 2% to 16%.
• For large returns above 30%, it is not that accurate.

Or using colors where green is accurate and red is inaccurate, the rule of 72 works this well

0.5, 1, 2, 3 4, 5, 6, 7, 8, 9, 10 12,, 14, 15, 16, 18, 20, 25, 30,35, 40, ... .

Less common use: If you sum your returns over several years, even if they are not the same, your money has double when you hit 72.

Example: if you have annual returns (in percent) of 9, 12, -3, 5, 7, 18, 2, 4, 12, 15, this sums to 81. So you would have doubled your money and more in the last year wtih the 15% returns.

Mathematical underpinnings.
If I have time later I'll explain the math behind the rule of 72. For now see the Wikipedia entry.