The Rule of 72: Doubling Times in Your Head
Divide 72 by a growth rate and you get the years to double — accurate within a hair across ordinary rates. Where the rule comes from, how to use it in both directions, and the estimates it makes instant.
Published · Saving & Investing · 2 min read
Most compound-growth questions require a calculator; one shortcut answers a surprising share of them in your head. Divide 72 by the annual growth rate and you get, almost exactly, the years required to double. Money at 8% doubles in about 9 years; at 6%, 12 years; at 3%, 24. The rule is centuries old — it appears in Luca Pacioli's 1494 mathematics text — and it remains the best power-to-weight ratio in financial arithmetic.
Why 72
The exact doubling time at rate r is ln(2)/ln(1+r), and for ordinary rates that expression is closely approximated by 72/r (72 wins over the mathematically purer 69.3 because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12). Accuracy is excellent between roughly 4% and 12% — the range where most financial questions live — drifting only modestly outside it. For mental math, it is effectively exact.
Both directions, many uses
- Growth: a portfolio at 7% doubles in ~10 years — so a 35-year-old's balance has roughly three doublings before 65: $100,000 becomes $200,000, $400,000, $800,000. Seeing retirement as "how many doublings remain" is the fastest intuition for why early money matters most — the last doubling is worth all the previous ones combined.
- Erosion: at 3% inflation, purchasing power halves in ~24 years; a 1% advisory fee on a 7% return stretches doubling from ~10 years to ~12 — the fee drag restated as lost time.
- Reverse: a promise to double your money in 5 years implies 72/5 ≈ 14.4% annual returns — a claim you can now price, and usually doubt, in the time it takes to hear it.
- Debt: an unpaid balance at 24% doubles in three years. The rule works just as well against you.
A sniff test, not a spreadsheet
The rule assumes a steady compound rate — real returns arrive lumpy — so treat it as estimation, not planning. For the real thing, the compound interest calculator computes exact growth paths, and the investment calculator adds contributions. But for pricing a pitch, a fee, or an inflation headline in five seconds flat, 72 divided by the rate remains unbeaten.
Run your own numbers
More on saving & investing
- Time in the Market vs. Timing the Market: What Missing the Best Days Costs
- Inflation: The Tax Nobody Legislates
- Sequence of Returns Risk: Why the First Retirement Years Decide Everything
This article is general education, not tax, legal, investment, or financial advice. Figures used in examples are illustrations, not quotes or predictions. For decisions that depend on your full situation, talk to a qualified professional.