How long does it take for money to double?
Divide 72 by the yearly return and you get roughly the years it takes money to double. Type a return and an amount; the answer shows the rule, the exact figure and the year your amount doubles.
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Your answer
At 7% a year, money doubles in about 10.3 years (exactly 10.2 years).
- 10.3 yearsRule of 7272 ÷ 7%
- 10.2 yearsExactln 2 ÷ ln(1 + rate)
- €20,000€10,000 becomesby 2036, at 7% a year
The rule of 72 is a mental shortcut that is closest between 6% and 10%; the exact time uses the compound interest formula with yearly compounding. Before inflation, fees and tax.
| Return | Rule of 72 | Exact years |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 3% | 24.0 | 23.4 |
| 4% | 18.0 | 17.7 |
| 5% | 14.4 | 14.2 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 9% | 8.0 | 8.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
The investment calculator opens with this amount and return, so you can see the whole curve.
Illustration only, not investment advice. Assumes a steady return; real returns vary.
Doubling time: why 72, and when the rule is wrong
Money grows by a factor (1 + r) each year, so it doubles when (1 + r)ⁿ = 2, that is after n = ln 2 ÷ ln(1 + r) years. For small rates ln(1 + r) is close to r, and ln 2 is about 0.693, so n is roughly 69.3 ÷ r; 72 is used because it divides neatly by 2, 3, 4, 6, 8, 9 and 12.
The rule is slightly high for low rates and slightly low for high ones. At 2% it says 36 years against an exact 35; at 12% it says 6 against 6.1. Between 6% and 10% the error is a few months.
The same rule works for costs. Prices rising 3% a year halve what money buys in about 24 years, and a cost of 2% a year halves a balance that would otherwise stand still in about 35 years.
Questions and answers
How does the Rule of 72 work?
A shortcut for how long money takes to double: divide 72 by the yearly rate in percent. At 7% it says about 10.3 years; the exact answer is 10.2. At 2% it says 36 years against an exact 35. It works in reverse too: to double in 10 years takes about 7.2% a year. The page shows both the shortcut and the exact figure for your rate.
How accurate is it?
Within a few months for rates between about 4% and 12%, which covers most savings and investing questions. It drifts at the ends: at 24% it says 3 years where the exact answer is 3.2, and at 1% it says 72 years against an exact 69.7. The exact formula is ln 2 ÷ ln(1 + r), and the calculator uses that for its second answer.
Does it work for fees and inflation too?
Yes, for anything that compounds. Inflation of 3% halves what money buys in about 24 years. A fund fee of 1% a year takes about a tenth of the result over 10 years and about a quarter over 30 (7% against 6% a year, no deposits); the glossary compares 0.2% and 1% in the calculator. The rule also says why a return a few points lower makes such a difference over decades: each doubling takes years longer.