The Rule of 72: A 60-Second Compounding Shortcut
Want to estimate doubling time without a calculator? Divide 72 by your interest rate. Here's why the rule works, and where it breaks down.
The Rule of 72 is the most useful mental-math shortcut in finance. Divide 72 by your annual interest rate and you get the approximate number of years for your money to double under compound interest.
Doubling time ≈ 72 / rate
Quick examples
- 4% return → doubles in ~18 years
- 6% return → doubles in ~12 years
- 8% return → doubles in ~9 years
- 10% return → doubles in ~7.2 years
- 12% return → doubles in ~6 years
- 20% credit card APR → doubles your debt in ~3.6 years
Why does it work?
Compound interest doubles when (1 + r)^t = 2. Taking the natural log: t = ln(2) / ln(1 + r). For small rates, ln(1+r) ≈ r, so t ≈ ln(2) / r ≈ 0.693 / r.
Multiplying by 100 to convert from decimal to percentage: t ≈ 69.3 / rate. The
"72" is a slightly inflated version that compensates for the approximation error in the
typical 4–12% range — and 72 has the bonus of being highly divisible (2, 3, 4, 6, 8, 9, 12).
How accurate is it?
| Rate | Rule of 72 | Actual | Error |
|---|---|---|---|
| 2% | 36.0 yr | 35.0 yr | +2.9% |
| 5% | 14.4 yr | 14.2 yr | +1.4% |
| 8% | 9.0 yr | 9.0 yr | 0% |
| 12% | 6.0 yr | 6.1 yr | −1.7% |
| 25% | 2.88 yr | 3.11 yr | −7.4% |
Sweet spot is 4–14% — the rule is essentially exact. At very high or very low rates, error creeps in.
Useful variants
- Rule of 70: more accurate for rates < 6%. Most economists use 70 for inflation halving.
- Rule of 114: tripling time. Divide 114 by the rate.
- Rule of 144: quadrupling time. Divide 144 by the rate.
- Rule of 72 for inflation: at 3% inflation, prices double in ~24 years.
Mental math in action
Imagine someone asks: "If I invest $50,000 at 9% for 24 years, what's it worth?"
- 9% doubles in 72/9 = 8 years.
- 24 years = 3 doublings.
- $50K → $100K → $200K → $400K.
The actual figure: $419,684. You're within 5% — in 10 seconds, no calculator.
Try the precise calculation
Once you've estimated, plug your numbers into our cumulative interest calculator for the exact answer plus a year-by-year schedule and chart. The Rule of 72 gets you in the right ballpark; the calculator gets you to the cent.