The Rule of 72
A 400-year-old mental-math shortcut for estimating doubling time.
The Rule of 72 says: divide 72 by your annual interest rate (as a whole number) to estimate how many years it takes for your money to double.
At 6% per year, money doubles in about 72 / 6 = 12 years. At 9%, about 8 years. At 12%, about 6 years. At 1%, about 72 years. No calculator needed.
Where does 72 come from?
The actual doubling time for compounding is ln(2) / ln(1 + r), where r is the annual rate. For small rates (say, below about 20%), the natural log expansion of ln(1 + r) is close to r − r²/2 + …. The Rule of 72 is the first-order approximation ln(2) / r ≈ 0.693 / r, multiplied by 100 to keep the math in percent. 0.693 × 100 = 69.3, which rounds to 72 for a reason that turns out to be convenience: 72 has many small integer factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36), so it divides cleanly by the most common interest rates.
When is it accurate?
The Rule of 72 is most accurate in the 5%–12% range, where the error is well under 1%. Outside that range it drifts:
| Rate | Rule of 72 | Exact (ln 2 / ln(1+r)) | Error |
|---|---|---|---|
| 1% | 72.0 yr | 69.7 yr | +2.3 yr (+3.4%) |
| 3% | 24.0 yr | 23.4 yr | +0.6 yr (+2.5%) |
| 6% | 12.0 yr | 11.9 yr | +0.1 yr (+0.9%) |
| 8% | 9.0 yr | 9.0 yr | +0.0 yr (+0.2%) |
| 10% | 7.2 yr | 7.3 yr | -0.1 yr (-1.0%) |
| 15% | 4.8 yr | 4.96 yr | -0.16 yr (-3.3%) |
| 20% | 3.6 yr | 3.80 yr | -0.20 yr (-5.3%) |
Below 5% the rule overestimates doubling time (money doubles faster than the rule predicts). Above 15% it underestimates (money doubles faster still — exponential growth accelerates). At very low rates, a variant — Rule of 69.3 — is mathematically tighter, but 72 is what you'll see quoted.
When is it useful?
- Sanity-check marketing claims. "Earn 12% annually and double in 6 years" — is the doubling-time promise consistent with the rate? Rule of 72 lets you check in seconds.
- Estimate inflation impact. At 3% inflation, prices double in about 24 years. Useful for thinking about long-term planning horizons.
- Compare investments quickly. 8% doubles in 9 years; 10% doubles in 7 years. That's a 2-year head start — meaningful over a 30-year career.
- Debt. The same rule applies to debts that compound. At 20% APR (credit-card territory), balances double in under 4 years.
Try it yourself
Open the Compound Interest Calculator, type a starting principal of 1000, a growth rate of 8, and a number of periods equal to 72/8 = 9. The "Future Value" should land close to 2000. It won't be exact (8% compounding is closer to 1.999), but it will be close enough to plan with.
For an annuity (you add money every period), the math is different — there's no simple Rule-of-72 analog, and you should use the calculator instead of guessing.
Caveats
- The Rule of 72 assumes continuous compounding-like growth. Real-world nominal annual rates usually compound monthly or quarterly, which slightly shifts the answer.
- It assumes a constant rate. Variable-rate investments (variable annuities, some bonds) will deviate.
- It ignores fees and taxes. A "7% return" with a 1% annual fee is more like 6%, and Rule of 72 on 6% gives 12 years, not 10.3.
- It only handles the first doubling. To go from $1,000 to $4,000 you need two doublings — so roughly 2× the doubling time, not 4×.
Related tools
- Compound Interest Calculator — exact future value with optional periodic contributions.
- Present Value Calculator — discount a future amount to today.
- Loan Calculator — monthly payments and full amortization schedule.
- NPV / IRR Calculator — discount-cash-flow analysis for any series.