The Rule of 72: Doubling Your Money in Your Head

A shortcut five centuries old

The Italian mathematician Luca Pacioli described the rule in his 1494 book Summa de arithmetica. He presented it without proof, which suggests merchants were already using it. The rule is still taught today because it turns a logarithm problem into simple division.

Years to double ≈ 72 ÷ annual rate (in %)

At 6% a year, money doubles in about 72 ÷ 6 = 12 years. At 9%, about 8 years. At 3%, about 24 years.

How close is it?

The exact doubling time for annual compounding is ln(2) ÷ ln(1 + r). Here is how the shortcut compares:

The rule is almost exact around 8% and drifts slowly in either direction. For everyday planning between about 4% and 12%, the error is a few months at most.

Why 72 and not 69.3?

The mathematically ‘pure’ constant is 69.3, because ln(2) ≈ 0.693. That version is exact for continuous compounding. With annual compounding, the true constant creeps upward as rates rise, and 72 lands close to it for common rates. It also has a practical advantage: 72 divides evenly by 2, 3, 4, 6, 8, 9, and 12, so the arithmetic stays easy.

Some people prefer 70 for low rates such as 1% to 3%, where it is slightly more accurate. All three versions are approximations of the same idea.

It works on debt and inflation too

• Credit card debt at 24% a year, left unpaid with interest compounding, roughly doubles in about 3 years.
• Prices rising at 3% a year roughly double in about 24 years — which also means a dollar’s purchasing power roughly halves over that time.
• A business growing revenue 12% a year roughly doubles in about 6 years.

Limits of the rule

The rule assumes a steady rate and reinvested growth. Real investments rarely deliver a constant return, fees and taxes reduce the effective rate, and deposits or withdrawals change the picture entirely. Treat it as a quick sense check, then use a full calculation for decisions.