The Rule of 72: Estimate Doubling Time in Your Head

The Rule of 72 says your money doubles in roughly 72 ÷ your annual return years — at 7% that’s about 10.3 years, and the mathematically exact answer is 10.24. It’s the rare mental shortcut that’s fast enough to use in conversation and accurate enough to trust for real planning estimates.

How do you use the Rule of 72?

Divide 72 by the annual return percentage, and the result is the approximate number of years to double. Earning 6%? Doubling takes about 12 years. Earning 10%? About 7.2 years. It also runs in reverse: if you want your money to double in 8 years, you need roughly a 9% annual return (72 ÷ 8).

The same trick works on the forces working against you. At 3% inflation, prices double — meaning your cash loses half its purchasing power — in about 24 years. A credit card at 24% doubles what you owe in roughly three years if nothing is paid down.

Where does 72 come from?

The 72 comes from the mathematics of exponential growth: the exact doubling time is $t = \frac{\ln 2}{\ln(1 + r)}$, and for small rates $\ln(1+r) \approx r$, which gives $t \approx \frac{0.693}{r}$ — the “Rule of 69.3.” Written with the rate as a percentage, that’s 69.3 divided by the percentage rate.

So why does everyone use 72 instead of 69.3? Two reasons, one mathematical and one practical:

1. The approximation $\ln(1+r) \approx r$ slightly understates doubling time, and the error grows with the rate. Nudging 69.3 up toward 72 happens to correct for this almost perfectly in the 6–10% range where most investment questions live.
2. 72 is a mental-math gift. It divides evenly by 2, 3, 4, 6, 8, 9, and 12 — exactly the rates people actually ask about. Dividing 69.3 by 8 in your head is nobody’s idea of a shortcut.

How accurate is it?

The Rule of 72 is accurate to within a few months across the whole range of realistic returns — here it is against the exact logarithmic answer:

Two patterns are worth noticing. In the heart of the table — 4% to 10% — the estimate lands within about a third of a year of the truth, which is far more precision than any forecast of future returns deserves anyway. At the extremes the drift shows: at very low rates the rule slightly overestimates doubling time (69.3 would fit better), and at high rates like 15% it drifts the other way. If you ever need the exact number, the Rule of 72 calculator computes both side by side.

What are its limits?

The Rule of 72 assumes a steady annual return, and real investments don’t cooperate. A portfolio averaging 7% doesn’t grow 7% every year — it lurches, and the rule says nothing about the path, only the destination implied by the average. It also works with nominal returns unless you feed it a real (inflation-adjusted) rate; money that doubles in 10.3 years at 7% has not doubled in purchasing power if inflation ran 3% the whole time (see Inflation and Real Returns).

Finally, the rule is only about doubling. For “how long until I reach a specific goal with monthly contributions,” you need the full future-value math — which is what the calculator and the savings calculator are for.

Why the rule is worth knowing anyway

The Rule of 72 earns its keep because it makes exponential growth feel concrete without a spreadsheet. Knowing that 7% doubles money every decade turns abstract percentages into a story: a 25-year-old’s dollar can double four times by 65, while a 45-year-old’s dollar gets two doublings — which is another way of seeing why starting early dominates almost every other decision. Any tool that makes that intuition instant is worth the tiny error bars.