The Rule of 72: A 500-Year-Old Trick for Seeing How Fast Money Grows

In 1494 a Franciscan friar in Venice published a vast compendium of mathematics, much of it written for merchants. Tucked inside, with no explanation, was a shortcut that still works: to find how long money takes to double, divide 72 by the interest rate.

How it works

At 6% a year, 72 ÷ 6 = 12, so savings double in about 12 years. That was the friar’s own example. He was Luca Pacioli, better known today for the first printed description of double-entry bookkeeping. The exact answer is 11.9 years.

The rule works for anything that grows by a steady percentage: savings, debts, prices, populations. It also runs backwards. If something doubled in nine years, 72 ÷ 9 tells you it grew by about 8% a year.

It assumes the rate holds steady, which investment returns never do. Treat the answer as a sense of scale, not a forecast.

Why 72?

The exact formula needs logarithms, which nobody could do in their head at a market stall. For small rates, the doubling time is close to 69.3 divided by the percentage, because 69.3 is 100 times the natural logarithm of 2. Economists often round it to 70.

Seventy-two trades a little precision for convenience. It divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and it partly corrects for interest being added once a year rather than continuously. At 8% it is almost perfect: 9 years against a true 9.01. Between about 4% and 12% it stays within 2% of the right answer. It drifts at the extremes: at 20% it says 3.6 years when the truth is 3.8.

Nobody knows who first noticed it. Pacioli gives no derivation, which suggests it was already in use among merchants before he wrote it down.

Three places it changes the picture

Inflation. At 3% inflation, prices double in about 24 years. Cash kept in a drawer for that long buys roughly half as much.

Debt. A balance charging 24% a year, left unpaid, doubles in about three years. The same arithmetic that grows savings works just as hard against a borrower.

Fees. The gap between earning 7% and 6% a year looks trivial. But at 7% money doubles roughly every 10 years, and at 6% every 12. Over 40 years, £10,000 grows to about £150,000 at 7% and about £103,000 at 6%. One percentage point, lost to fees every year, takes nearly a third of the final sum.

The takeaway

A percentage on its own hides how much it matters. Whenever something compounds, whether a savings rate, a loan, inflation or a fee, divide it into 72. A number of years is much easier to feel than a percentage.