The rule of 72

Compound growth is hard to picture. A rate of 6% a year does not sound very different from 8%, and neither gives much sense of what happens over decades. The rule of 72 turns a rate into something easier to grasp: the time it takes to double.

How it works

Divide 72 by the annual rate, written as a whole number. The result is the approximate number of years for the amount to double.

Annual rate	Rule of 72	Exact answer
3%	24 years	23.4 years
6%	12 years	11.9 years
8%	9 years	9.0 years
12%	6 years	6.1 years

The estimate is close across the range of rates most people meet. It drifts at very high rates, where it should not be relied on.

Why 72

The exact doubling time comes from a logarithm, and for small rates it works out to a little over 69 divided by the rate. The number 72 is used instead because it gives a slightly better answer at everyday rates and because it divides evenly by 2, 3, 4, 6, 8, 9 and 12.

What it is good for

The rule makes differences between rates concrete. At 6% money doubles in 12 years, so over 36 years it doubles three times and becomes eight times the original. At 8% it doubles four times in the same 36 years and becomes sixteen times the original. Two percentage points, over a long enough period, is the difference between eight and sixteen.

It works in the other direction as well. Inflation of 3% halves the buying power of cash in about 24 years. A debt charging 24% doubles in about three.

The rule is an approximation and ignores taxes, fees and rates that change over time. Its value is in the first rough answer, the one that tells you whether a precise calculation is worth doing.