The Rule of 72: How Fast Does Money Double?
The Rule of 72 is a mental shortcut. Divide 72 by an annual growth rate in percent, and the answer is roughly how many years it takes for an amount to double when it compounds at that rate. At 6% a year, 72 ÷ 6 = 12, so money doubles in about 12 years.
It needs no calculator, which makes it useful for sanity checks. This guide shows how accurate it is, where the number 72 comes from, and how the same trick works for debt, prices and the rate you would need to hit a goal.
How to use the rule
years to double ≈ 72 ÷ annual rate (in percent)Use the rate as a whole number: 8% means 8, not 0.08.
Doubling time: at 9% a year, 72 ÷ 9 = 8 years. At 3% a year, 72 ÷ 3 = 24 years.
Required rate: turn the rule around. To double an amount in 10 years you need roughly 72 ÷ 10 = 7.2% a year. The exact answer is 7.18%, so the shortcut is off by only 0.02 points.
A faster target: to double in 6 years, 72 ÷ 6 = 12% a year is needed. The exact rate is 12.25%, so a plan built on 12% would fall a little short. The rule is best used to judge whether a goal is realistic, not to set a precise deadline.
Several doublings: each doubling takes the same time at the same rate. At 8% a year, doubling takes about 9 years, so 27 years is three doublings, or about 2 × 2 × 2 = 8 times the starting amount. The exact figure is 1.0827 = 7.99.
How accurate is it?
The exact doubling time for a rate r (as a decimal) is ln 2 ÷ ln(1 + r). Here is the rule next to the exact value:
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 years | 35.00 years |
| 3% | 24.0 years | 23.45 years |
| 4% | 18.0 years | 17.67 years |
| 6% | 12.0 years | 11.90 years |
| 8% | 9.0 years | 9.01 years |
| 10% | 7.2 years | 7.27 years |
| 12% | 6.0 years | 6.12 years |
| 18% | 4.0 years | 4.19 years |
The rule is closest in the middle, around 6% to 10%, where it is within about a tenth of a year of the exact answer. It slightly overstates the time at low rates and understates it at high rates. At 24% it says 3.0 years against an exact 3.22.
Why 72 and not 69 or 70?
For small rates, ln(1 + r) is close to r, so the doubling time is close to ln 2 ÷ r. Since ln 2 is about 0.693, that gives 69.3 ÷ rate (in percent), which is the most accurate version for very low rates or continuous compounding. Some people use 70 for the same reason, because it is easier to divide.
The number 72 is a compromise. It is slightly higher than 69.3, which corrects for the way the approximation drifts at typical rates of 6% to 10%. It is also divisible by 2, 3, 4, 6, 8, 9 and 12, so common rates divide cleanly: 72 ÷ 8 = 9, 72 ÷ 12 = 6, 72 ÷ 4 = 18.
For tripling, a similar shortcut is about 114 ÷ rate. At 8% it gives 14.25 years against an exact 14.27.
Using it beyond savings
- Inflation: at 3% a year, prices double in about 72 ÷ 3 = 24 years, which also means money loses half its purchasing power over that time. See inflation and purchasing power.
- Debt: a balance that grows at 18% a year with no payments doubles in about 4 years (exact 4.19).
- Fees: a cost of 1 percentage point a year shifts a 7% return to 6%. The doubling time then moves from about 10.3 years (72 ÷ 7) to 12 years (72 ÷ 6), so a seemingly small fee adds close to two years to every doubling.
- Population or any steady growth: the rule works for any quantity that grows by a constant percentage per period, not only money.
When you need an exact figure, or want to include regular deposits, switch to the compound interest calculator. For a goal-based version, the future value calculator shows how a balance builds up.
Limits to keep in mind
- It assumes a constant rate. Real returns on investments vary from year to year.
- It assumes you add and withdraw nothing and that interest compounds at least yearly.
- It ignores taxes and fees, which lower the effective rate you should plug in.
- It gets less reliable above about 20% a year.
This article is general education, not financial advice. A doubling-time estimate is arithmetic, not a forecast of what any investment will do.
- Compound Interest Calculator: Enter a starting balance, an interest rate and a term to see how money grows when interest is added to the balance. Add regular deposits or withdrawals to model a savings plan.
- Future Value Calculator: Enter a starting amount, how long it stays invested, an interest rate and how often it compounds. Add a regular deposit or withdrawal if you like, and see what the money grows to.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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