The Rule of 72: A Quick Way to Estimate Doubling Time
How the Rule of 72 works, how accurate it really is compared to the exact compound interest formula, and worked examples at several interest rates.
The Rule of 72 is a mental-math shortcut for estimating how long it takes an investment to double at a given annual growth rate, without needing a calculator or logarithms.
The rule
Years to double ≈ 72 ÷ annual interest rate. At 7% annual growth: 72 ÷ 7 ≈ 10.3 years.
How accurate is it?
| Rate | Rule of 72 estimate | Exact years to double |
|---|---|---|
| 3% | 24.0 years | 23.4 years |
| 5% | 14.4 years | 14.2 years |
| 7% | 10.3 years | 10.2 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
The Rule of 72 stays within a few tenths of a year of the exact answer across typical real-world interest rates (roughly 3-15%), which is why it's a genuinely useful quick estimate rather than just a rough approximation.
Why it works (briefly)
It's derived from the natural logarithm form of the compound interest formula — ln(2) ÷ ln(1 + r) — and 72 happens to be a convenient round number close to 100 × ln(2) ≈ 69.3 that also divides evenly by many common rates (2, 3, 4, 6, 8, 9, 12), making the mental math easier than using the more precise 69.3.
For an exact answer rather than an estimate — including with monthly contributions, which the Rule of 72 doesn't account for at all — use the Compound Interest Calculator.