The rule, in one breath
Take the yearly rate — a savings yield, an investment return, an interest charge — and divide 72 by it. The answer is the number of years for the amount to double. Money in an account paying 4% doubles in about 18 years. An investment returning 8% doubles in about 9. A balance growing at 12% doubles in about 6. That is the whole rule, and it has been passed around since at least 1494, when Luca Pacioli printed it in his Summa de Arithmetica as a thing merchants simply knew.
Why it works — and why 72
Compounding means each year's growth itself grows the next year, and doubling time turns out to depend on the rate in a neat, nearly proportional way. The mathematically pure constant is about 69.3 — it falls out of the logarithm of 2 — but 72 compensates slightly for yearly (rather than continuous) compounding at everyday rates, and it has a second virtue that matters more: divisibility. Seventy-two splits evenly by 2, 3, 4, 6, 8, 9 and 12, which covers nearly every rate a person actually meets, so the one division the rule asks for comes out clean, in your head, while you are still looking at the bank brochure.
How far off is it?
In the middle range — say 5% to 12% — the rule is usually within a few months of the exact answer, which is remarkable for something you can do while pouring coffee. It drifts at the edges. At 2% it promises 36 years against an exact 35. At 20% it promises 3.6 years against an exact 3.8. And it assumes a steady rate, while real investments wander up and down; treat its answer as the planning estimate it is, not a promise. That is why this page always prints the exact compounding figure beside the rule's answer — the shortcut for speed, the logarithm for truth.
The rule's darker uses
Doubling works the same for things you owe and things that erode. A card balance at 24% doubles in about 3 years if it is left alone — a sobering number to hold next to a minimum payment. Inflation at 4% means cash sitting idle loses half its buying power in about 18 years; at 3%, about 24. Retirees deciding how much cash to keep "safe" are really choosing a slow halving schedule, and the Rule of 72 makes that schedule visible in one division. Used this way the rule is less a party trick and more a small instrument of honesty.
Doubling more than once
Two doublings make four times the money; three make eight times. At 8%, the first doubling takes about 9 years, the second 9 more — so $10,000 becomes roughly $20,000 in 9 years, $40,000 in 18 and $80,000 in 27, before taxes, fees and life's interruptions. This is why starting early matters so much more than starting big: time is what supplies the doublings, and each one is worth as much as all the growth before it. Our Compound Interest Calculator shows the same growth year by year if you want the full picture.
Frequently asked questions
What is the Rule of 72?
A mental-math shortcut for compound growth: divide 72 by the yearly interest or return rate, and the answer is roughly how many years money takes to double. At 6%, 72 ÷ 6 = 12 years. At 9%, about 8 years.
How accurate is the Rule of 72?
Very good in the range most people meet — roughly 5% to 12% — where it is usually within a few months of the exact answer. It drifts at extremes: at 2% it says 36 years against an exact 35, and at 20% it says 3.6 years against an exact 3.8.
Why 72 and not some other number?
The mathematically pure constant would be about 69.3, but 72 is close at common interest rates and divides neatly by 2, 3, 4, 6, 8, 9 and 12 — the rates people actually meet — so the division is easy to do in your head.
Does the Rule of 72 work for debt and inflation too?
Yes — anything growing or shrinking at a steady percentage. A credit card balance at 24% doubles in about 3 years if nothing is paid. Inflation at 4% halves the buying power of idle cash in about 18 years.
Where did the Rule of 72 come from?
It appears in Luca Pacioli's Summa de Arithmetica, published in 1494, stated as a known rule of thumb. It is often credited to Albert Einstein, with a quote about compound interest being the eighth wonder of the world — there is no evidence he ever said it, but the rule hardly needs a famous name to be useful.