The Rule of 72 Explained

The Rule of 72 is the most useful piece of financial arithmetic you can do without a calculator.

Divide 72 by the annual rate. The answer is the years it takes money to double.

Examples

At 6%, money doubles in 12 years. At 8% it takes 9 years, and at 12% just 6.

At 2% inflation, prices double in 36 years. At 6% inflation, in 12.

Where it comes from

Doubling means (1 + r)^t = 2. Taking logs gives t = ln(2) / ln(1 + r).

ln(2) is 0.693. For small rates ln(1 + r) is close to r, so t is about 69.3 / rate.

72 is used instead of 69 because it divides neatly by 2, 3, 4, 6, 8, 9 and 12.

How accurate it is

Between 6% and 10% the rule is within a few months of the exact answer. At 8% it is almost perfect.

At very low rates 69 or 70 works better. At rates above 20% the rule overstates the time.

Using it in reverse

Want to double your money in 10 years? You need 72 / 10, or about 7.2% a year.

Want to quadruple it? That is two doublings, so 20 years at 7.2%.

More

The doubling time tables list exact figures at every rate. The Rule of 72 calculator does the division for you.