Rule of 72 Explained: Formula, Calculator & Accuracy
Rule of 72 explained: divide 72 by a positive effective annual rate to estimate doubling time. At 8%, about 9 years; compare exact math and limits.
The Rule of 72 is a shortcut for estimating how many years a balance takes to double: divide 72 by a positive annual rate written as a whole-number percentage. At a steady 8% effective annual growth rate, the estimate is about 9 years (72 / 8), while annual compounding gives an exact result of about 9.01 years. Use the rate table for a quick comparison and the logarithmic formula when precision matters; this is a scenario, not a return forecast. Try the Rule of 72 calculator for an exact comparison.
Compare the Rule of 72 estimate with the exact logarithmic doubling time for your rate.
A mental-math shortcut that estimates doubling time by dividing 72 by a positive annual rate written as a whole-number percentage.
Example: At a constant 8% effective annual rate, 72 / 8 estimates 9 years to double.
For annual compounding at effective annual rate r, the exact time is t = ln(2) / ln(1 + r), where r is a decimal.
Example: At 8%, ln(2) / ln(1.08) is about 9.01 years.
The growth rate over one full year after compounding. A nominal APR may need conversion before using the Rule of 72.
Rule of 72 explained in plain terms: for a single starting balance growing at a steady, positive effective annual rate, divide 72 by the rate to estimate the doubling time. It assumes the rate stays constant and does not include deposits, withdrawals, taxes, or fees.
Rule of 72 formula
Estimated years to double = 72 / R, where R is the annual effective rate written as a whole percentage. At 8%, divide 72 by 8 for an estimate of 9 years.
Rule of 72 vs Rule of 70 vs Rule of 76 vs exact ln(2)/ln(1+r)
Drag the rate slider. See which mental-math rule is most accurate at that rate, and how long it really takes to double, triple, and 8× your money.
| Method | Years to double | Error vs exact | Best for |
|---|---|---|---|
| Rule of 70 70 ÷ 8.0 | 8.75 | -2.8% | Low rates (1–5%) |
| Rule of 72 72 ÷ 8.0 | 9.00 | -0.1% | Typical rates (6–10%)← winner here |
| Rule of 76 76 ÷ 8.0 | 9.50 | +5.5% | High rates (15%+) |
| Exact: ln(2) / ln(1+r) The mathematically true answer | 9.01 | 0.0% | Requires a calculator |
See accuracy band across all rates (1% – 25%)
| Rate | Rule 70 err | Rule 72 err | Rule 76 err |
|---|---|---|---|
| 1% | 0.5% | 3.4% | 9.1% |
| 2% | 0.0% | 2.8% | 8.6% |
| 3% | 0.5% | 2.3% | 8.0% |
| 5% | 1.5% | 1.4% | 7.0% |
| 7% | 2.4% | 0.4% | 6.0% |
| 8% | 2.8% | 0.1% | 5.5% |
| 10% | 3.7% | 1.0% | 4.5% |
| 12% | 4.6% | 1.9% | 3.5% |
| 15% | 5.9% | 3.2% | 2.2% |
| 20% | 7.9% | 5.3% | 0.0% |
| 25% | 9.9% | 7.3% | 2.1% |
Green = lowest error at that rate. Rule of 70 wins below 4%, Rule of 72 wins 5–12%, Rule of 76 wins above 18%.
Compare the estimate with the exact result
With annual compounding, a balance after t years is P x (1 + r)^t. Set that equal to 2P and solve: exact years = ln(2) / ln(1 + r), where r is the effective annual rate as a decimal. The shortcut uses R = 100 x r and replaces the exact calculation with 72 / R.
How accurate is the Rule of 72?
- At 2%: the estimate is 36 years; the exact annual-compounding result is 35.00 years, so the estimate is about 2.9% longer.
- At 4%: 18 years versus 17.67 years, about 1.9% longer.
- At 8%: 9 years versus 9.01 years, less than 0.1% shorter.
- At 12%: 6 years versus 6.12 years, about 1.9% shorter.
- At 15%: 4.8 years versus 4.96 years, about 3.2% shorter.
- At 24%: 3 years versus 3.22 years, about 6.9% shorter.
What the estimate assumes
The rate is constant and positive, and the balance is left invested without extra deposits or withdrawals. Investment returns vary over time, so this calculation describes a fixed-rate scenario; it does not predict when a real portfolio will double.
Monthly compounding and quoted rates
Use an effective annual growth rate. If a product quotes a nominal APR compounded m times per year, convert it to an effective annual rate first: (1 + APR / m)^m - 1. An APY is already an effective annual rate, so do not compound it a second time. For precision, use the exact doubling-time formula with the converted rate.
Does it include monthly contributions?
No. The Rule of 72 estimates how one starting balance grows. Regular deposits change the calculation; use our compound interest calculator to include a starting balance, monthly contribution, rate, and timeline.
Inflation and purchasing power
The same shortcut estimates how long prices take to double at a constant inflation rate. At 3% effective annual inflation, 72 / 3 gives about 24 years; the exact annual-compounding result is about 23.45 years. Actual inflation changes from year to year.
Use the calculator
Enter a rate in the Rule of 72 calculator to compare the shortcut with an exact result. The Rule of 72 table lists more rates; use the exact formula when precision matters.
Frequently asked questions
What is the Rule of 72?
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What is the Rule of 72 and how do you calculate it?
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How accurate is the Rule of 72?
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Does the Rule of 72 work with monthly compounding?
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Does the Rule of 72 include monthly contributions?
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Can I apply it to variable investment returns?
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How long does purchasing power take to halve at 3% inflation?
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Sources & further reading
Using this guide in a lesson, report or article? See citation formats and link to this specific page with its assumptions and review date.
Plug in your own amounts with our free calculators.