The two formulas
Rule of 72: Years ≈ 72 / annual rate
Exact formula: Years = ln(2) / ln(1 + r) where r = rate as decimal
Error comparison
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36 yrs | 35.0 yrs | +2.9% |
| 4% | 18 yrs | 17.7 yrs | +1.7% |
| 8% | 9 yrs | 9.0 yrs | 0.0% |
| 12% | 6 yrs | 6.1 yrs | −1.4% |
| 20% | 3.6 yrs | 3.8 yrs | −4.5% |
| 50% | 1.44 yrs | 1.71 yrs | −16% |
For most practical financial decisions at rates under 20%, the Rule of 72 is close enough. For rates above 20% (high-growth companies, high-interest debt), use the exact formula.
The Rule of 72 calculator shows both values side by side so you can see the difference for any rate.