Rule of 72 vs Rule of 69 Comparison Calculator
Enter an interest rate and instantly compare all three doubling-time estimates side-by-side: Rule of 72, Rule of 69.3, and the exact continuous compounding formula.
Rule of 72 vs Rule of 69.3 — What's the Difference?
The Rule of 72 is the most popular mental math shortcut in personal finance: divide 72 by the annual interest rate to get the approximate number of years to double your money. At 6% it's 12 years; at 9% it's 8 years. The number 72 was chosen because it has many divisors (2, 3, 4, 6, 8, 9, 12), making mental arithmetic easy.
The Rule of 69.3 uses the natural log of 2 (ln 2 ≈ 0.6931) and is mathematically exact for continuously compounded interest: doubling time = 69.3 / r. It is less convenient to divide mentally but significantly more accurate at very high or very low rates. The exact formula for periodic annual compounding is ln(2) / ln(1+r), which this calculator uses as the baseline comparison. Last updated: May 2026.
When to Use Which Rule
| Scenario | Best Rule | Reason |
|---|---|---|
| Quick mental math (6–10% rate) | Rule of 72 | Easiest to divide, small error <1% |
| Continuous compounding (savings, bonds) | Rule of 69.3 | Mathematically exact for continuous |
| Very high rates (>15%) | Exact formula | Both rules diverge significantly |
| Very low rates (<3%) | Rule of 69.3 | Rule of 72 overestimates by 2–3 years |
Practical Examples
A stock index fund returning 10% per year: Rule of 72 gives 7.2 years, the exact formula gives 7.27 years — an error of less than 0.1 years, negligible for planning. At 2% (high-yield savings account), Rule of 72 gives 36 years while the exact formula gives 35.0 years — still close. At 25% (venture-stage return target), Rule of 72 gives 2.88 years while the exact formula gives 3.11 years — a 0.23-year difference that matters for IRR-sensitive decisions. In those cases, use the exact calculator above or Rule of 69.3 for a better estimate.
Frequently Asked Questions
What is the Rule of 72?
The Rule of 72 is a quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 8% interest, 72/8 = 9 years. It works best for rates between 6% and 10%.
What is the Rule of 69.3 and when is it more accurate?
The Rule of 69.3 uses ln(2) ≈ 0.693 and gives the exact doubling time for continuously compounded interest: 69.3/r. It is more mathematically precise than Rule of 72 for continuous compounding, but harder to divide mentally.
Which rule is most accurate — 72, 69, or 69.3?
For continuous compounding, the exact formula ln(2)/ln(1+r) is most accurate. Rule of 69.3 matches continuous compounding exactly. Rule of 72 is closest to accuracy for periodic compounding at typical rates of 6–10%.
Does the Rule of 72 work for annual or monthly compounding?
The Rule of 72 was designed for annual compounding. It gives a reasonable approximation for monthly compounding too. For continuous compounding use Rule of 69.3.
Can I use the Rule of 72 for debt too?
Yes. If you carry a credit card balance at 24% APR, 72/24 = 3 years to double your debt. This makes the Rule of 72 a powerful way to visualize the cost of high-interest debt.