Divide 72 by your interest rate and you get roughly the years it takes money to double. This calculator runs the famous shortcut alongside the exact formula, in both directions.
Rule of 72 estimate
10.3 yrs
72 ÷ 7 — $10,000 becomes $20,000
Exact answer
10.24 yrs
ln(2) ÷ ln(1 + r), with annual compounding
| Rate | Rule of 72 | Exact doubling time |
|---|---|---|
| 1% | 72.0 yrs | 69.7 yrs |
| 2% | 36.0 yrs | 35.0 yrs |
| 4% | 18.0 yrs | 17.7 yrs |
| 7% | 10.3 yrs | 10.2 yrs |
| 10% | 7.2 yrs | 7.3 yrs |
| 12% | 6.0 yrs | 6.1 yrs |
Give it a rate and it returns the doubling time — 72 ÷ rate as the mental-math estimate, and ln(2) ÷ ln(1 + r) as the exact compound-interest answer. Flip the mode and it solves the other way: how big a return you need for your money to double within a set number of years.
Doubling at a compound rate r takes ln(2)/ln(1+r) years, and for realistic rates that is close to 69.3/r. The number 72 stuck because it's nearly as accurate in the 4–12% range and divides cleanly by 2, 3, 4, 6, 8, 9, and 12. At 8%, the rule says 9 years; the exact answer is 9.01. The table above shows how tight the estimate stays.
The rule cuts both ways: at 3% inflation, prices double — meaning your cash's buying power halves — in about 24 years. See that effect on real dollars with the inflation calculator, and see what realistic bank rates do to your balance with the savings interest calculator.
A mental-math shortcut: 72 divided by an annual growth rate approximates the years for a sum to double. At 6%, money doubles in about 72 ÷ 6 = 12 years. It works for investment returns, savings interest, inflation, or any compound growth.
Very good between roughly 4% and 12% — usually within a couple of months of the exact answer. At very low rates 69.3 is mathematically truer, and at very high rates the rule increasingly overestimates; this calculator always shows the exact figure alongside.
At a 4% APY, about 18 years (72 ÷ 4). At the 0.01% many big banks pay, about 7,200 years — a vivid argument for moving idle cash to a high-yield account.
Yes — divide 72 by the inflation rate to see how quickly prices double, which is the same as how quickly cash loses half its buying power. At 3% inflation, that's roughly every 24 years.
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