Rule of 72 Calculator
The Rule of 72 is a fast mental-math shortcut for estimating how long an investment takes to double at a fixed annual return. Just divide 72 by the interest rate: at 8%, your money doubles in about 9 years.
At 7% per year, it takes roughly 10.3 years for your money to double.
Where the Rule of 72 comes from
The rule is an approximation of the exact compound-interest doubling condition
2 = (1+r)t, whose solution is t = ln(2) / ln(1+r).
Because ln(2) ≈ 0.693 and ln(1+r) ≈ r for small r,
the doubling time is roughly 0.693 / r — and 72 is a convenient numerator
because it's divisible by many common rates (6, 8, 9, 12). Under this rule the
doubling time tracks the exact formula within a few percent for rates between about
4% and 12%.
When the rule breaks down
At very high rates (above ~20%), the approximation drifts because
ln(1+r) no longer equals r. At very low rates it actually
overestimates doubling time slightly. For anything outside the 4%–12% band, prefer
the full compound interest calculator on this site.