In short
- Years to double ≈ 72 ÷ annual return percentage. At 8% that is 9 years, and the exact answer is 9.01.
- The approximation is most accurate around 8%, overstates slightly below it, and understates slightly above.
- It also works in reverse: 72 ÷ years gives the return needed to double in that time.
- Applied to inflation instead of returns, it gives the time for prices to double — at 3%, about 24 years.
The rule
Years to double ≈ 72 ÷ annual return (%) Return needed ≈ 72 ÷ years available 6% → 12 years 12 years → 6% 9% → 8 years 8 years → 9%
That is the whole thing. It exists because the exact calculation requires logarithms, and 72 happens to be a number with a lot of small divisors — 2, 3, 4, 6, 8, 9, 12 — which makes the division easy to do without a calculator.
How accurate it is
The exact doubling time is ln(2) ÷ ln(1 + r). Compared against it, the rule behaves like this:
| Return | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36.0 years | 35.0 years | +1.00 |
| 4% | 18.0 years | 17.7 years | +0.33 |
| 6% | 12.0 years | 11.9 years | +0.10 |
| 8% | 9.0 years | 9.0 years | −0.01 |
| 10% | 7.2 years | 7.3 years | −0.07 |
| 12% | 6.0 years | 6.1 years | −0.12 |
| 15% | 4.8 years | 5.0 years | −0.16 |
| 20% | 3.6 years | 3.8 years | −0.20 |
It is essentially exact at 8%, and stays within about four months of the truth across the 4–15% band that covers almost every realistic planning assumption. It degrades at very low rates — at 1% it is more than two years out — and drifts the other way at very high ones.
Why 72 and not 69: The mathematically exact constant for continuous compounding is closer to 69.3. For annual compounding at realistic rates, 72 is a better fit — and it divides cleanly by far more numbers, which is the entire point of a mental shortcut.
What it is useful for
- Sanity-checking a projection. If a calculator says a portfolio quadruples in 15 years at 7%, that implies two doublings in 15 years, or roughly 10 years each. The rule says 10.3. The projection is plausible.
- Understanding inflation. At 3% inflation, prices double in about 24 years. At 5%, about 14. This is often more intuitive than a percentage.
- Seeing what a fee costs. A portfolio at 7% doubles in about 10.3 years; at 5.5% it takes 13.1. Over a long horizon that gap is a missed doubling.
- Comparing rates quickly. The difference between 6% and 8% sounds small until it is expressed as 12 years against 9.
What it does not do: The rule handles a single lump sum growing at a constant rate. It says nothing about ongoing contributions, withdrawals, taxes, fees, or variable returns — and it describes an assumed rate, not a rate anyone is guaranteed to receive.
Frequently Asked Questions
What is the rule of 72?
A mental shortcut for how long an investment takes to double: divide 72 by the annual percentage return. At 6% it gives 12 years, against an exact answer of 11.9. It works in reverse too — 72 divided by the number of years gives the return required to double in that time.
How accurate is the rule of 72?
Very accurate in the middle of the realistic range. It is essentially exact at 8% and stays within about four months of the true figure between 4% and 15%. It overstates the doubling time below 8% and understates it above, and becomes unreliable at very low rates — at 1% it is more than two years out.
Why is it 72 rather than another number?
The mathematically exact constant is nearer 69.3 for continuous compounding, but 72 fits annual compounding better at realistic rates and divides evenly by 2, 3, 4, 6, 8, 9, and 12. Ease of mental division is the reason the rule is useful at all.
Can the rule of 72 be used for inflation?
Yes, in the same way. Dividing 72 by the inflation rate gives the number of years for prices to roughly double — about 24 years at 3%, and about 14 at 5%.
Does it account for contributions?
No. It describes a single amount compounding at a constant rate with nothing added or removed. Any projection involving regular contributions, withdrawals, fees, or taxes needs a proper calculation rather than the shortcut.
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The information and calculations provided are for informational and educational purposes only and should not be considered financial, investment, or professional advice. Projections are hypothetical, based on assumptions that may not reflect actual market conditions. Past performance does not guarantee future results, and all investments carry risk of loss. Consult a qualified financial professional before making financial decisions.