Rule of 72 calculator
How long money takes to double at a given return — the mental shortcut, and the exact answer beside it.
Time to double
10.2 years
the rule of 72 says 10.29 years
- Rule of 72 estimate
- 10.3 years
- Error in the rule
- 0 years
- Time to quadruple
- 20.5 years
| Starting amount | $25,000 |
|---|---|
| Doubled | $50,000 |
| Quadrupled | $100,000 |
At 7% money doubles in 10.24 years; the rule of 72 says 10.29 — close enough to do in your head, and wrong at the extremes.
How this is calculated
How this is calculated
The shortcut
Divide 72 by the percentage rate. At 8% that is 9 years, at 6% it is 12. The number 72 is chosen because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is what makes it usable without a calculator.
years ≈ 72 / rateThe exact answer
Doubling time is ln 2 divided by ln(1 + rate). The rule is within about 0.1 years between 6% and 10%, and drifts badly outside it: at 25% the rule says 2.9 years against an exact 3.1.
years = ln 2 / ln(1 + r)Worked example: $25,000 at 7%
| Amount | $25,000 |
|---|---|
| Return | 7% |
| Doubles in | 10.24 years |
|---|---|
| Rule of 72 says | 10.29 years |
| Quadruples in | 20.5 years |
Two doublings take twice as long as one, so $25,000 becomes $100,000 in about 20 years and $200,000 in 30.
What this assumes
- The return is constant every year.
- Returns compound annually.
- No deposits, withdrawals or fees.
- Figures are before inflation and tax.
Where this commonly goes wrong
- The rule is calibrated for rates near 8%. Below 3% or above 20% the error is large enough to matter for planning.
- Doubling in nominal terms is not doubling in buying power: at 2.8% inflation the real doubling time at 7% is closer to 17 years.
- A 1% fee changes a 7% return to 6%, which pushes doubling from 10.2 years to 11.9 — nearly two years for one percentage point.
Questions
How long does money take to double at 7%?
About 10.2 years. The rule of 72 gives 10.29, which is close enough for a mental estimate. Two doublings — quadrupling — takes about 20.5 years, and three takes just under 31.
Why 72 and not 69 or 70?
The mathematically exact numerator at low rates is about 69.3. Seventy-two is used because it divides cleanly by so many small integers, which is the entire point of a rule you do in your head.
Does the rule work for debt?
Yes, and it is more alarming that way. A 21.9% credit card doubles the balance in about 3.3 years if nothing is repaid, which is why minimum payments on a card take so long to make progress.
Does it work for inflation?
It does. At 3% inflation prices double in about 24 years — which is the useful way to think about a retirement 30 years out, where today’s costs will have more than doubled.
When is the rule most wrong?
At very high and very low rates. At 1% the rule says 72 years against an exact 69.7; at 25% it says 2.88 against 3.11. Between 6% and 10% the error is under a tenth of a year.
What about the rule of 114 and 144?
Same idea for other multiples: divide 114 by the rate for tripling, 144 for quadrupling. All three are approximations of the same logarithm and drift the same way at the extremes.
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This calculator does arithmetic on the figures you enter. It does not account for tax, fees, or your personal circumstances.
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