What is the rule of 72
Updated on June 30, 2026 · by Rafael Rossi
The rule of 72 is the most useful shortcut in personal finance: divide 72 by the rate and you get how many periods money takes to double. No calculator, no logarithms, and an error of a few percent across the range that matters.
The rule
time to double ≈ 72 ÷ rate (in % per period)
At 8% a year, money doubles in 72 ÷ 8 = 9 years. At 1% a month, it doubles in 72 months, or six years.
The unit of the rate sets the unit of the answer: a monthly rate returns months, an annual rate returns years. Mixing the two is the only mistake available here.
Where the 72 comes from
The exact calculation is time = ln(2) ÷ ln(1 + i). Since ln(2) ≈ 0.693 and, for small rates, ln(1+i) ≈ i, the time lands around 69.3 ÷ rate.
So the "correct" number would be 69.3. We use 72 for two reasons: it compensates for the approximation at somewhat larger rates and — decisively — 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the arithmetic possible in your head at almost every common rate.
Where the rule is right and where it drifts
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 1% | 72.0 | 69.7 | +3.4% |
| 2% | 36.0 | 35.0 | +2.8% |
| 4% | 18.0 | 17.7 | +1.9% |
| 6% | 12.0 | 11.9 | +0.9% |
| 8% | 9.0 | 9.01 | −0.1% |
| 12% | 6.0 | 6.1 | −1.9% |
| 20% | 3.6 | 3.8 | −5.3% |
| 30% | 2.4 | 2.6 | −9.2% |
The rule is practically perfect at 8% and stays excellent between 4% and 12% — which happens to be exactly the range of investment returns where people use it. Outside that band the error grows, and above 20% the rule turns too optimistic: it promises doubling sooner than it happens.
For very low rates some prefer 69 or 70; for high ones, 76. But swapping the constant sacrifices the rule's greatest virtue, which is being doable without paper.
The variants: 114 and 144
- Rule of 114 — tripling. At 8% a year: 114 ÷ 8 = 14.3 years. The exact value is 14.27. Essentially spot on.
- Rule of 144 — quadrupling. That is just doubling twice, so it equals 2 × 72.
The use that alarms people: inflation
The rule works just as well for measuring the destruction of value, and that is where it usually stings.
At 5% annual inflation, the purchasing power of idle cash halves in 14.4 years (the exact figure is 14.2). At 10% a year, in a little over 7. Apply that to money sitting in a checking account and the result is an invisible tax nobody explicitly charged.
The same logic covers debt. A credit card balance at 24% APR doubles in three years — 72 ÷ 24 = 3. It is the fastest calculation available for understanding why a revolving balance should not be carried.
A less obvious use: finding the rate
The rule inverts effortlessly. If you know how long something took to double, rate ≈ 72 ÷ time.
A house that doubled in price over 12 years appreciated about 6% a year — a much less impressive figure than "it doubled in value", and one you can immediately compare against any other investment over the same period.
How many doublings you have left
There is a way of using the rule that reorganises how you think about retirement. Instead of counting years, count doublings.
At 8% a year, money doubles every 9 years. So someone aged 30 planning to stop at 65 has 35 years, or nearly 4 doublings: $10,000 invested today becomes about $148,000. Starting at 40 leaves 25 years, or 2.8 doublings: the same $10,000 becomes $68,000. Starting at 50 leaves 1.7 doublings, and reaches $32,000.
Ten years of delay cost more than half the result, with the same money and the same rate. It is the bluntest way to see that time is the most expensive input in this calculation — and the only one you cannot buy later.
Frequently asked questions
Does it work with monthly contributions? No. The rule applies to a single sum growing at compound interest. With contributions the balance doubles far faster, because part of the growth is new money rather than return.
Should I use the nominal or the real rate? It depends what you want to know. The nominal rate tells you how long the number takes to double; the real rate (net of inflation) tells you how long purchasing power takes to double. For long-term planning, the second is the right question.
Does it work for negative returns? Not directly, but the reasoning adapts: a 10% annual decline halves the value in about 7 years — and keeps halving every 7, without ever reaching zero.
Why not just use the exact formula? Do, when you have a calculator. The rule of 72 exists for the moment you are in a conversation, hearing a pitch, and need to know in five seconds whether the number makes sense. It is a detection tool, not an accounting one.