Rule of 72
Finance's most famous mental shortcut: divide 72 by the interest rate to get the years it takes to double your money — or the other way around. With the exact math shown.
Why 72, of all numbers?
The mathematically correct number would be 69.3 (that is, 100 × ln 2), but 72 won out for pure convenience: it divides evenly by 2, 3, 4, 6, 8, 9 and 12, so the typical cases work out in your head with no calculator. At 6% your money doubles in about 12 years, at 8% in 9, at 12% in 6. The rule also runs in reverse — 72 divided by the years gives the rate you'd need — and it even works for inflation: at 3% a year, the purchasing power of your cash is cut in half in roughly 24 years.
Where the rule breaks down
It's an approximation, and its accuracy depends on the rate: it's excellent between 4% and 12%, but at very low rates the right divisor is closer to 69–70, and at very high rates the rule underestimates the years. Above all, it assumes a constant return compounded every year — in real life returns swing around, and taxes, fees and inflation eat into the result. That's why this tool also shows the exact calculation, ln 2 / ln(1 + rate), so you can see how good the shortcut really is.
This tool provides estimates for educational purposes only: it is not a prediction of returns and is not financial advice.