Rule of 72 Calculator
Rule of 72: years to double your money at a yearly rate (72 ÷ rate), the exact time and the rules of 70 and 69.3, or the rate that doubles it in a set time. How it works
Use the Rule of 72 Calculator
About the Rule of 72 Calculator
At 8% a year money doubles in about 9 years: 72 ÷ 8 = 9.0. The exact time, ln 2 ÷ ln(1.08), is 9.01 years. The rule of 72 calculator shows both, compares the rules of 70 and 69.3, and works back from a number of years to the rate needed to double.
Years to double by yearly interest rate
| Yearly rate | Rule of 72 | Exact | Rule of 72 off by |
|---|---|---|---|
| 1% | 72.00 | 69.66 | +3.4% |
| 2% | 36.00 | 35.00 | +2.8% |
| 3% | 24.00 | 23.45 | +2.3% |
| 4% | 18.00 | 17.67 | +1.9% |
| 5% | 14.40 | 14.21 | +1.4% |
| 6% | 12.00 | 11.90 | +0.9% |
| 7% | 10.29 | 10.24 | +0.4% |
| 8% | 9.00 | 9.01 | -0.1% |
| 9% | 8.00 | 8.04 | -0.5% |
| 10% | 7.20 | 7.27 | -1.0% |
| 12% | 6.00 | 6.12 | -1.9% |
| 15% | 4.80 | 4.96 | -3.2% |
| 20% | 3.60 | 3.80 | -5.3% |
Years, with interest compounded once a year. A plus sign means the rule gives a longer time than the exact one.
Rate needed to double money in a number of years
| Years to double | Rule of 72 | Exact rate |
|---|---|---|
| 3 | 24.00% | 25.99% |
| 5 | 14.40% | 14.87% |
| 6 | 12.00% | 12.25% |
| 8 | 9.00% | 9.05% |
| 10 | 7.20% | 7.18% |
| 12 | 6.00% | 5.95% |
| 15 | 4.80% | 4.73% |
| 20 | 3.60% | 3.53% |
Rule: 72 ÷ years. Exact: (2^(1 ÷ years) − 1) × 100, compounded yearly.
Frequently asked questions
- How long does it take to double money at 6%?
- 12 years by the rule of 72 (72 ÷ 6) and 11.90 years exactly. At 10% the rule gives 7.20 years and the exact time is 7.27.
- What interest rate doubles money in 10 years?
- 7.20% a year by the rule (72 ÷ 10). The exact rate is 7.18%. To double in 5 years the rule says 14.40% and the exact rate is 14.87%.
- How accurate is the rule of 72?
- Within about 1% of the exact time for rates of 6% to 10%: at 6% it is 0.9% long and at 10% 1.0% short. At 20% it is 5.3% short (3.60 years against 3.80), and at 1% it is 3.4% long.
- Which is better, the rule of 72, 70 or 69.3?
- It depends on the rate. Below about 1%, 69.3 is closest. From about 1% to 5% the rule of 70 is: at 2% it gives 35.00 years, the same as the exact time. From about 5% up, 72 is closer: at 8% it gives 9.00 years against an exact 9.01, while 70 gives 8.75 and 69.3 gives 8.66. At high rates all three come out short.
- Can I use the rule of 72 for inflation?
- Yes. At 3% inflation prices double in about 24 years by the rule (72 ÷ 3) and in 23.45 years exactly, so a dollar then buys half what it buys now. Enter the inflation rate as the rate.
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