Rule of 72
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The most useful shortcut in finance: divide 72 by your growth rate and you get the years to double your money. It works in your head, this shows the shortcut and the exact answer side by side.
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Why 72 works
Money doubling at rate r takes ln(2) ÷ ln(1+r) years, not mental math. But ln(2) ≈ 0.693, and for everyday rates the compound term is nearly linear, so 72 ÷ rate lands remarkably close. 72 (rather than 69.3) is chosen because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12.
Quick table
8% → 9 · 10% → 7.2 · 12% → 6
It cuts both ways
The rule also measures decay: at 3% inflation, prices double, and cash halves, in about 24 years. Accuracy is best between roughly 4% and 15%; outside that band, trust the exact figure shown alongside. For the full mechanics, see compound interest and CAGR.
Rule of 72 FAQ
A mental shortcut: divide 72 by an annual growth rate to estimate the years for money to double. At 8%, about 9 years. It also reverses, divide 72 by a number of years to get the rate required.
Very good for rates between about 4% and 15%, usually within a few months of the exact answer. It drifts at extreme rates, which is why this calculator shows the true logarithmic answer alongside.
The mathematically exact constant is about 69.3 (from ln 2), but 72 is nearly as accurate at typical rates and divides cleanly by many small numbers, making the mental arithmetic trivial.
Yes, it estimates any compounding process. At 3% inflation, prices double roughly every 24 years, which equally means cash loses half its buying power in that time.