8% a year
About 9 years by the rule; 9.01 years exactly.
Rule of 72 calculator
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Returns compound once a year at a steady rate. The rule of 72 is a shortcut; the exact figure uses logarithms. Taxes, fees and inflation are not included.
%
10 thousand
Years to double
9.0 years
At 8% a year, 72 ÷ 8 = 9.0 years. The exact answer is 9.01 years. $10,000 becomes $20,000 in that time.
- Rule of 72
- 9.00 years
- Exact
- 9.01 years
- Rate needed to double in 10 years
- 7.18%
Years to double at common rates
| Rate | Rule of 72 | Exact | Difference |
|---|---|---|---|
| 1% | 72.0 | 69.7 | 2.34 |
| 2% | 36.0 | 35.0 | 1.00 |
| 3% | 24.0 | 23.4 | 0.55 |
| 4% | 18.0 | 17.7 | 0.33 |
| 5% | 14.4 | 14.2 | 0.19 |
| 6% | 12.0 | 11.9 | 0.10 |
| 7% | 10.3 | 10.2 | 0.04 |
| 8% | 9.0 | 9.0 | -0.01 |
| 9% | 8.0 | 8.0 | -0.04 |
| 10% | 7.2 | 7.3 | -0.07 |
| 12% | 6.0 | 6.1 | -0.12 |
| 15% | 4.8 | 5.0 | -0.16 |
Doubling your money in your head
The rule of 72 is one of the few finance shortcuts worth memorising. Divide 72 by the yearly rate and you get roughly the number of years for money to double. At 8%, 72 ÷ 8 = 9 years, so $10,000 becomes about $20,000.
The exact answer uses logarithms: ln 2 ÷ ln 1.08 = 9.01 years. At 6%, the rule says 12 years and the exact answer is 11.9. The table under the result shows how close the two stay for common rates, and where they drift apart.
It is just as useful for costs. Credit card debt at 24% doubles in about 3 years if nothing is paid. Inflation at 3% halves what money buys in about 24 years, which is why cash in a savings account at 1% loses ground.
Run it backwards to test a promise. If someone says an investment will double in 4 years, it needs a return of about 18% a year, which is well above what stock markets have paid on average. Treat claims like that with care.
Sources
What this calculator does not account for
- The shortcut drifts at very low or very high rates.
- Assumes a steady yearly return.
How this is calculated
Formula: Rule of 72
years to double ≈ 72 ÷ rate; exact years =ln 2 ÷ ln(1 + rate ÷ 100)What the symbols mean
- rateThe yearly return or interest rate, in percent.
- lnThe natural logarithm.
Good to know
- The shortcut is closest between about 6% and 10%.
- It works in reverse too: 72 ÷ years gives the rate needed to double in that time.
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Worked examples
Each example is worked out by the same code as the calculator above.
6% a year
12 years by the rule; 11.9 years exactly.
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<iframe src="/embed/rule-of-72-calculator" title="Rule of 72" width="100%" height="720" style="border:0;max-width:42rem" loading="lazy"></iframe>Questions
What is the rule of 72?
A shortcut for how long money takes to double: divide 72 by the yearly rate. At 8%, it takes about 9 years.
How accurate is the rule of 72?
Very close for rates between about 6% and 10%. At 8% it gives 9 years against an exact 9.01. It drifts at very low or very high rates.
What rate do I need to double my money in 10 years?
About 7.2% by the rule, and 7.18% exactly.
Does the rule of 72 work for inflation?
Yes. At 3% inflation prices double in about 24 years, so the money in your pocket buys half as much.
What about the rule of 70 or 69?
They are variants. 69.3 is the most precise for continuous compounding; 72 is used because it divides easily by many numbers.