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The Rule of 72 is off by a full year at 2%. Here is the exact doubling time.
Everyone quotes the Rule of 72 — almost nobody checks it. The shortcut (72 ÷ rate) is nearly perfect near 8% but drifts a full year high at savings-account rates and months low at high returns. This calculator shows the exact doubling time (ln(2) ÷ ln(1+r)) next to the rule, runs it in reverse (what return doubles your money in your target years), and flips it around to show inflation quietly halving your purchasing power on the same math.
Anyone quoting the 72 shortcut uses it to see the exact answer beside the estimate — the rule is off a full year at savings-account rates — and the inflation flip: at 3%, idle cash loses half its purchasing power every 23.4 years. It turns a cocktail-party rule into a precision tool.
Best near 8%: it says 9.00 years, the exact answer is 9.01. It drifts from there — at 2% it overestimates by a full year (36 vs 35.0 exact), at 6% by 1.3 months, and at 20% it underestimates by 2.4 months (3.6 vs 3.8 exact). For anything beyond cocktail-party math, use the exact formula: years = ln(2) ÷ ln(1 + rate).
69.3 is the "true" constant (100 × ln 2) and is exactly right only for continuous compounding. Annual compounding needs a slightly bigger number, and 72 wins on convenience: it divides cleanly by 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36. The happy accident is that 72 lands almost exactly on the right answer for annual compounding near 8%.
Exactly 7.18% per year (2^(1/10) − 1) — the Rule of 72 reverse guess (72 ÷ 10 = 7.2%) is close. To double in 5 years you need 14.87% per year, a return no honest investment promises consistently, which is why "double your money in 5 years" pitches are a red flag. The same math runs against you with inflation: at 3% inflation, cash loses half its purchasing power every 23.4 years whether you invest it or not.