The rule of 72
Divide 72 by the annual interest rate and you get roughly the number of years it takes an investment to double. At 8% a year, 72 ÷ 8 = 9 years; the exact answer with annual compounding is 9.006 years. The rule is popular because 72 divides evenly by so many common rates: 2, 3, 4, 6, 8, 9 and 12.
Why it works
Doubling means (1 + r)^t = 2, so t = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, and ln 2 ≈ 0.693, giving t ≈ 69.3 ÷ rate. Rounding the numerator up to 72 compensates for annual compounding at typical rates.
Other uses
- Inflation: at 4% inflation, prices double, and your money's purchasing power halves, in about 18 years.
- Debt: a credit card at 24% doubles an unpaid balance in about 3 years.
- Growth: an economy growing 3% a year doubles in output in about 24 years.
The page also shows the rules of 70 and 69.3, which are closer at low rates and for continuous compounding.
How this works
The headline is 72 divided by the rate. The exact figure is the natural logarithm of 2 divided by the natural logarithm of (1 + rate ÷ 100), which assumes interest compounds once a year. The rules of 70 and 69.3 are shown for comparison; 69.3 is exact for continuous compounding. Everything runs in your browser.
Frequently asked
What is the rule of 72?
A shortcut: 72 ÷ annual rate ≈ years for money to double.
How accurate is it?
Very close between about 6% and 10%. At 8% it gives 9 years against an exact 9.006.
When should I use 70 or 69.3?
At low rates or with continuous or daily compounding, 70 or 69.3 is closer.
Does it work for inflation?
Yes. 72 ÷ inflation rate is roughly how long until prices double.
Sources
Reviewed Oct 17, 2026 · test vectors fixtures/calculators/finance/rule-of-72-calculator/