How to Use the Rule of 72

Estimates in your head how long compound interest takes to double the principal: 72 ÷ the annual rate as a percentage. The exact answer is ln2 ÷ ln(1 + rate), but at rates of a few per cent, dividing 72 does the job.

This estimates in your head how many years compound interest takes to double the principal.

\text{years} \approx \dfrac{72}{\text{annual rate (\%)}}

The exact answer comes from the formula below, which needs a calculator. Dividing 72 does not.

\text{years} = \dfrac{\ln 2}{\ln(1 + r)}

Why 72

Since $\ln 2 = 0.693$ , dividing 69.3 approaches the exact answer at very small rates. As the rate climbs, compounding pushes the years needed up a little. Splitting the difference, 72 fits best across the range of a few per cent. It also divides neatly by 2, 3, 4, 6, 8 and 9, which helps in mental arithmetic.

Example

At 6%, $72 \div 6 = 12$ years, against an exact 11.90: a gap of a tenth of a year. At 8% the rule gives 9 years and the exact answer is 9.01. Tripling takes 18.85 years.

Notes

The fit is good from roughly 4% to 15%. At 1% the rule says 72 years where the exact answer is 69.7, and at 30% it says 2.4 against 2.64, so the gap starts to show.

The same idea works for inflation. At 3% a year, money halves in value in 24 years.