The Rule of 72: mental math for doubling your money
One division, no calculator, no spreadsheet: divide 72 by an annual rate of return and you get roughly the number of years it takes for money to double. It is the most useful piece of arithmetic in personal finance, and it takes about ten seconds to learn.
Published August 7, 2026 · updates automatically with our data
The trick
At 3% a year, money doubles in about 24.0 years. At 7%, about 10.3 years. At 10%, about 7.2 years. That is the whole rule: 72 ÷ rate = years to double. The exact answers are 23.4 and 7.3 years for 3% and 10% — close enough that the shortcut is worth trusting for anything you would work out in your head.
It works because compounding is exponential, and the natural logarithm of 2 is about 0.693. Doubling time is really 69.3 ÷ rate, but 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and the small overshoot happens to correct for the error the linear shortcut introduces at everyday rates. Between roughly 4% and 12% the rule is accurate to a few months.
What it does to a lifetime
Take the real thing. From 1979 to 2025 the S&P 500 compounded at about 9.4% a year — a doubling roughly every 7.6 years by the rule, 7.7 years if you do the exact calculation. Over those 46 years that is about 6 doublings, which is why a single unremarkable-looking deposit made in the late seventies became a life-changing sum by now without anyone doing anything clever.
The rule also runs backwards, which is where it stings. Inflation is a rate too. At 3% inflation, prices double in 24.0 years and the purchasing power of cash held under a mattress halves in the same time. Our inflation time machine shows what that has actually done to your currency.
The part the average hides
That 9.4% is an average across 46 years, and averages are smooth in a way that markets never are. Over the same period the index fell in 11 of 46 years, and its worst single year, 2008, took 38.5% off the index. Anyone who needed their money in one of those years met a very different number from the average. Nobody earns the average in any given year; they earn it only by being present for all of them, including the bad ones.
So use the rule for what it is good at — sanity-checking a plan, comparing two savings rates, seeing whether a fee matters — and not as a forecast. A 1% annual fee turns 7% into 6%, and 72 ÷ 6 = 12 years: the 10.3-year doubling now takes a year longer. That is the kind of question the rule answers in one breath.
Try the exact version
When the mental shortcut is not enough — monthly contributions, a specific target, a real time horizon — the compound interest calculator does the full month-by-month arithmetic and charts the curve. It also makes the honest point visible: most of the growth arrives in the final doublings, which is the real argument for starting early rather than for picking winners.
Open the compound interest calculator →
MoneyCurio is an educational project. Nothing here is financial or investment advice; figures are approximations built from public data — see the methodology page for sources.