At 8% a year, the rule of 72 gives 72 ÷ 8 = 9.0 years to double; the exact answer is 9.01 years.
- Rule of 72 (years)
- Exact (years)
| Annual rate | Rule of 72 (years) | Exact (years) | Gap (years) |
|---|---|---|---|
| 1% | 72.0 | 69.66 | 2.34 |
| 2% | 36.0 | 35.00 | 1.00 |
| 3% | 24.0 | 23.45 | 0.55 |
| 4% | 18.0 | 17.67 | 0.33 |
| 5% | 14.4 | 14.21 | 0.19 |
| 6% | 12.0 | 11.90 | 0.10 |
| 7% | 10.3 | 10.24 | 0.04 |
| 8% | 9.0 | 9.01 | -0.01 |
| 9% | 8.0 | 8.04 | -0.04 |
| 10% | 7.2 | 7.27 | -0.07 |
| 12% | 6.0 | 6.12 | -0.12 |
| 15% | 4.8 | 4.96 | -0.16 |
| 18% | 4.0 | 4.19 | -0.19 |
| 20% | 3.6 | 3.80 | -0.20 |
| 24% | 3.0 | 3.22 | -0.22 |
How it is computed
Rule of 72: years ≈ 72 ÷ rate (%). Exact: years = ln 2 ÷ ln(1 + rate), with annual compounding. The gap column is the rule minus the exact value.
FAQ
When is the rule of 72 accurate?+
Between about 6% and 10% it is within a few weeks. At low rates it overstates the time slightly, and at high rates it understates it.
Does it work for inflation or debt?+
Yes. At 3% inflation prices double in about 24 years, and a debt at 24% doubles in about 3 years if nothing is paid.