Rule of 72 Calculator
Rule of 72 Calculator
How long money takes to double at a given rate — by the rule of 72, by the exact formula, and how far apart the two are. The same arithmetic tells you how fast inflation halves what money buys.
Years to double
Money growing at 12% a year
The rule, and the exact figure it approximates
- R
- the annual rate in percent, compounded once a year
- ln 2
- 0.6931 — the reason 69.3 is the exact number for continuous compounding
Worked example
Money growing at 12% a year
Rule of 72: 72 ÷ 12 = 6.0 years
Exact: ln 2 ÷ ln 1.12 = 0.6931 ÷ 0.1133 = 6.12 years
The rule is 0.12 years (1.9%) short of the exact figure
At 4% inflation prices double, and money's buying power halves, in 17.67 years; the rule says 18
Years to double, by rule and exactly (compounded yearly)
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact | Closest rule |
|---|---|---|---|---|---|
| 1% | 72.00 | 70.00 | 69.30 | 69.66 | 70 |
| 2% | 36.00 | 35.00 | 34.65 | 35.00 | 70 |
| 3% | 24.00 | 23.33 | 23.10 | 23.45 | 70 |
| 4% | 18.00 | 17.50 | 17.32 | 17.67 | 70 |
| 6% | 12.00 | 11.67 | 11.55 | 11.90 | 72 |
| 8% | 9.00 | 8.75 | 8.66 | 9.01 | 72 |
| 10% | 7.20 | 7.00 | 6.93 | 7.27 | 72 |
| 12% | 6.00 | 5.83 | 5.77 | 6.12 | 72 |
| 15% | 4.80 | 4.67 | 4.62 | 4.96 | 72 |
| 20% | 3.60 | 3.50 | 3.46 | 3.80 | 72 |
| 25% | 2.88 | 2.80 | 2.77 | 3.11 | 72 |
Why 72, and when 70 or 69.3 is better
Money compounding at R% a year doubles when (1 + R ÷ 100)years = 2, so the exact answer is ln 2 ÷ ln(1 + R ÷ 100). For small rates ln(1 + x) is close to x, which gives 69.3 ÷ R. That is why 69.3 is the exact rule for continuous compounding. Over the rates people actually earn, yearly compounding needs a slightly bigger number: the number that would be exact climbs from 69.3 towards 72 at about 7.8%, and passes it above that. 72 is also easy to divide by 2, 3, 4, 6, 8, 9 and 12, which is why it became the rule.
So which rule to use depends on the rate. Below about 1.0%, 69.3 is closest; from there to about 4.9%, 70; above that, 72 is the best of the three, though it runs increasingly short at high rates. At 12% the rule says 6 years and the truth is 6.12. Beyond about 20% none of the rules is reliable; use the exact figure shown under the result.
The same arithmetic works in reverse for inflation. Prices rising at 4% a year double in about 17.7 years, which means a fixed sum of money buys half as much. A pension, a salary or savings that do not grow lose half their purchasing power in that time. At 6% it is about 11.9 years.
The rule is for a steady rate compounded once a year. Investment returns are neither steady nor guaranteed, so treat any doubling time as an illustration. To see a whole sum grow year by year, use the lumpsum calculator or the compound interest calculator; to work out the rate an investment actually earned, the CAGR calculator. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
What is the rule of 72?
A shortcut: years to double ≈ 72 ÷ the annual rate in percent. At 12% that is 6 years; the exact figure is 6.12.
Is the rule of 70 or the rule of 72 more accurate?
It depends on the rate. With yearly compounding the rule of 70 is closer between about 1.0% and 4.9%, and the rule of 72 above that. For continuous compounding, 69.3 is exact.
How does the rule of 72 apply to inflation?
Divide 72 by the inflation rate to find roughly how long it takes prices to double, and money’s buying power to halve. At 4% that is about 18 years; exactly 17.67.
Does it work for any rate?
It works best between about 5% and 12%. At very high rates it understates the doubling time noticeably; the exact figure is shown under the result.
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References
- U.S. Securities and Exchange Commission, Investor.gov. Glossary: Rule of 72. https://www.investor.gov/introduction-investing/investing-basics/glossary/rule-72
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. McGraw-Hill. Compound interest, effective annual rates, continuous compounding and the future value of an annuity.
- Central-bank inflation targets used as default inflation by currency: Reserve Bank of India (4% CPI, flexible inflation targeting framework); U.S. Federal Reserve (2% PCE); European Central Bank (2%); Bank of England (2% CPI); Bank of Canada (2%); Reserve Bank of Australia (2–3%); Bangko Sentral ng Pilipinas (3% ± 1). Actual inflation often runs above target.