The Rule of 72 formula
The Rule of 72 is a shortcut for compound doubling time. Divide 72 by the percentage rate to get the years to double, or divide 72 by the years to get the required rate:
years to double ≈ 72 ÷ rate(%)
rate(%) to double ≈ 72 ÷ years
The exact doubling time comes from solving (1 + r)t = 2, which gives t = ln 2 ÷ ln(1 + r). The "72" is a clean approximation because 100 × ln 2 ≈ 69.3, and 72 divides evenly by many small numbers.
Worked example
An investment earning 8% a year:
Rule of 72: 72 ÷ 8 = 9.0 years to double.
Exact: ln 2 ÷ ln(1.08) = 0.6931 ÷ 0.0770 = 9.01 years.
So $10,000 becomes about $20,000 in roughly 9 years, then $40,000 in 18 years.
Doubling time at common rates
| Return | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 yr | 35.0 yr |
| 4% | 18.0 yr | 17.7 yr |
| 6% | 12.0 yr | 11.9 yr |
| 8% | 9.0 yr | 9.0 yr |
| 10% | 7.2 yr | 7.3 yr |
| 12% | 6.0 yr | 6.1 yr |
Note: the Rule of 72 assumes a fixed rate and reinvested returns, and ignores taxes, fees and inflation. It's a quick estimate, not a guarantee.