Rule of 72
Brainteasers & GuesstimatesA mental shortcut: divide 72 by a growth rate to get the number of years an amount takes to double.
Divide 72 by the annual growth rate expressed as a whole number and you get the approximate years to double. At 9% it is 8 years, at 12% it is 6, at 6% it is 12.
It works because it approximates the logarithms involved in compounding, and it is accurate enough for mental use across roughly 5% to 20%. Outside that range it drifts.
It runs backwards just as usefully. If something doubled in five years, it grew at roughly 72 divided by 5, or about 14% a year, which is often the faster route to an answer in an interview.
In a buyout context, the related conversions are worth knowing outright: 2.0x over three years is about 26%, over five about 15%, 2.5x over five about 20% and 3.0x over five about 25%.
Worked example
At 9% a year, 72 divided by 9 is 8, so money doubles in about eight years. The exact answer is 8.04 years.
Run backwards: something that doubled in five years grew at roughly 72 divided by 5, or about 14.4% a year. The exact figure is 14.9%.
It drifts outside roughly 5% to 20%. At 40%, the rule says 1.8 years against a true 2.1, so use it where it works and say so where it does not.