The Rule of 72
Compound growth doubles on a fixed schedule set entirely by the rate, and that schedule is a logarithm — not the kind of thing most people calculate in their head. The Rule of 72 approximates it with a single division, close enough for everyday planning across the range of rates most savings and investment products actually offer.
Formulas
Exact: Years = ln(2) ÷ ln(1 + rate)
72 was chosen historically because it divides evenly by more small numbers than nearby alternatives like 70 or 69 — by 2, 3, 4, 6, 8, 9, and 12 — which made it easier to compute by hand before calculators existed. The exact constant for continuous compounding is closer to 69.3, which is where the Rule of 69 comes from for anyone who wants a marginally more precise shortcut at low rates.
Where the Approximation Holds and Where It Breaks Down
The rule is a linear approximation of a curved relationship, so it is exact nowhere and close almost everywhere that ordinary interest rates live.
6% to 10% — the sweet spot
Error stays under a few weeks across this band, which covers most long-run stock market return assumptions and many investment product illustrations.
Below 4% — still usable, slightly optimistic
The rule predicts a shorter doubling time than the exact figure at low rates, by a small but growing margin as the rate falls further.
Above 15% — the gap widens noticeably
At high rates, common in credit card debt, the rule's estimate diverges further from the exact answer. Use the exact figure shown above rather than the mental shortcut once a rate reaches double digits.
Beyond a Single Doubling
The same shortcut extends past one doubling: money doubles again after the same interval, so it quadruples in twice the Rule of 72 estimate, and increases eightfold in three times it. This is why long, uninterrupted compounding periods matter so much more than they intuitively seem to — each additional doubling period adds as much growth as every one before it combined.
The rule runs the other direction too, for inflation: dividing 72 by an inflation rate estimates how many years until prices double, or equivalently how long until a fixed sum of money loses half its purchasing power. At 3% inflation, that is roughly 24 years — well within a typical working lifetime.