Finance
The Rule of 72: How Accurate Is It?
How the Rule of 72 estimates doubling time, why 72 works, an accuracy table against the exact answer from 1% to 30%, and the rules of 70 and 69.3.
By TooleemPublished Facts checked
Short answer
The Rule of 72 says money doubles in about 72 ÷ the annual interest rate years: at 8% a year, 72 ÷ 8 = 9 years, and the exact answer is 9.01. It is accurate to within about 2% for rates between 3% and 12%, which covers most savings and investment returns. Below 3% it overstates the time a little (use 70 instead), and above 15% it understates it by 3% to 9%.
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The rule in one line
years to double ≈ 72 ÷ annual rate (in %)
It works in reverse too. To double your money in 6 years you need about 72 ÷ 6 = 12% a year. The rule assumes the return compounds once a year and stays the same every year; it says nothing about risk.
Why 72 works
The exact doubling time solves (1 + r)^t = 2, so t = ln 2 ÷ ln(1 + r). For small rates ln(1 + r) is close to r, which gives t ≈ 0.693 ÷ r, or 69.3 ÷ the rate in percent. That is the exact rule for continuous compounding.
t = ln 2 ÷ ln(1 + r) ln 2 = 0.6931 t ≈ 69.3 ÷ rate%
With yearly compounding, ln(1 + r) falls further below r as the rate rises, so the best constant creeps up: 70.7 at 4%, 72.1 at 8%, 73.4 at 12%. People use 72 because it sits in the middle of typical rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12.
How accurate it is, rate by rate
| Rate | Exact years | Rule of 72 | Error (72) | Rule of 70 | Error (70) | Rule of 69.3 | Error (69.3) |
|---|---|---|---|---|---|---|---|
| 1% | 69.66 | 72.00 | +3.4% | 70.00 | +0.5% | 69.30 | −0.5% |
| 2% | 35.00 | 36.00 | +2.8% | 35.00 | 0.0% | 34.65 | −1.0% |
| 3% | 23.45 | 24.00 | +2.3% | 23.33 | −0.5% | 23.10 | −1.5% |
| 4% | 17.67 | 18.00 | +1.9% | 17.50 | −1.0% | 17.32 | −2.0% |
| 5% | 14.21 | 14.40 | +1.4% | 14.00 | −1.5% | 13.86 | −2.4% |
| 6% | 11.90 | 12.00 | +0.9% | 11.67 | −1.9% | 11.55 | −2.9% |
| 7% | 10.24 | 10.29 | +0.4% | 10.00 | −2.4% | 9.90 | −3.4% |
| 8% | 9.01 | 9.00 | −0.1% | 8.75 | −2.8% | 8.66 | −3.8% |
| 9% | 8.04 | 8.00 | −0.5% | 7.78 | −3.3% | 7.70 | −4.3% |
| 10% | 7.27 | 7.20 | −1.0% | 7.00 | −3.7% | 6.93 | −4.7% |
| 12% | 6.12 | 6.00 | −1.9% | 5.83 | −4.6% | 5.77 | −5.6% |
| 15% | 4.96 | 4.80 | −3.2% | 4.67 | −5.9% | 4.62 | −6.8% |
| 20% | 3.80 | 3.60 | −5.3% | 3.50 | −7.9% | 3.46 | −8.9% |
| 25% | 3.11 | 2.88 | −7.3% | 2.80 | −9.9% | 2.77 | −10.8% |
| 30% | 2.64 | 2.40 | −9.2% | 2.33 | −11.7% | 2.31 | −12.6% |
Two practical conclusions. Between 6% and 10% the Rule of 72 is off by about a month at most. For low rates, such as inflation or a savings account at 2%, the Rule of 70 is closer.
Tripling and quadrupling
The same idea extends: tripling takes about 115 ÷ rate years and quadrupling about 144 ÷ rate years (two doublings, 2 × 72).
| Rate | Triple: exact | Triple: 115 ÷ rate | Quadruple: exact | Quadruple: 144 ÷ rate |
|---|---|---|---|---|
| 6% | 18.85 | 19.17 | 23.79 | 24.00 |
| 8% | 14.27 | 14.38 | 18.01 | 18.00 |
| 10% | 11.53 | 11.50 | 14.55 | 14.40 |
Using it for inflation and debt
Anything that grows at a steady percentage doubles on the same schedule, including prices and unpaid debt.
- Inflation at 3% doubles prices in about 24 years (exact: 23.45). Put the other way, money kept in cash loses half its purchasing power in that time.
- A card balance at 2% a month doubles in 36 months by the rule, 35 months exactly, if nothing is paid. Use the monthly rate and the answer comes out in months.
- A fee of 1% a year on an investment returning 7% cuts the net rate to 6%: doubling slows from about 10.3 to 12 years.
Common mistake
Real returns are not constant
The rule assumes the same return every year. Investment returns vary, and a sequence of good and bad years can double much faster or much slower than 72 ÷ the average rate. Treat the result as a rough guide to the power of compounding, not a forecast.
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Sources
The figures and rules in this guide come from these documents.
- What is compound interest?Investor.gov, U.S. Securities and Exchange CommissionThe Rule of 72 as taught by the SEC: divide 72 by the expected rate of return (9% doubles in about 8 years).
Facts checked
General information, not legal, tax or financial advice. Rules change; check the cited sources for your own case.
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