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Rule of 72 — Doubling Time

How long money takes to double, and what the shortcut gets wrong.

Inputs
7%
Doubles in
10.24 years
Rule of 72 estimate
10.29 years
Shortcut error
+0.4%
Triples in
16.24 years
Ten-fold in
34.03 years
years ≈ 72 ÷ rate · exact = ln 2 ÷ ln(1 + rate)

At this rate the shortcut is within 1% of the exact answer — this is the band it was designed for.

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Divide 72 by the annual percentage rate for the years to double: at 8%, 72 ÷ 8 = 9 years. The exact figure is ln 2 ÷ ln(1 + rate), which at 8% gives 9.01 years — close enough for mental arithmetic.

How to use Rule of 72 Calculator

  1. Set the annual rate. The compounding rate on the investment, loan or inflation figure.
  2. Read the doubling time. The exact answer, with the rule-of-72 estimate and its error beside it.

About estimating doubling time

The rule of 72 is the most useful piece of mental financial arithmetic there is, because it converts a rate — which is abstract — into a length of time, which is not. Told that a fund returns 9%, most people have no intuition for what that means. Told that it doubles roughly every eight years, they immediately do. The constant is a compromise rather than a mathematical constant. The exact figure for continuous compounding is 69.3, but 72 was chosen because it divides evenly by more small numbers than anything nearby, which is the entire point of a shortcut you do in your head. It happens to fit annual compounding well in the 6 to 10% band and drifts outside it, underestimating at very low rates and overestimating at very high ones. The exact form — the natural log of 2 divided by the natural log of one plus the rate — is shown here beside it so the gap is visible rather than assumed away. It is worth applying the rule in the uncomfortable direction too. Inflation at 6% halves what your money buys in twelve years, and a debt at 18% doubles in four. The same arithmetic that makes compounding look attractive on the way up makes it alarming on the way down, and that second reading is usually the more actionable one.

Frequently asked questions

Why 72 and not 69?
The mathematically correct constant for continuous compounding is about 69.3, but 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which makes it far easier to do in your head. It also happens to fit annual compounding better in the 6 to 10% range where most people use it.
How accurate is the rule of 72?
Within about 1% for rates between roughly 6 and 10%. It drifts outward from there — at 1% it underestimates and at 25% it overestimates by several percent. For a mental estimate that is fine; for a decision that turns on the difference, use the exact figure.
Does it work for inflation?
Yes, and it is arguably more useful there. At 6% inflation, prices double in about twelve years, which is a more legible way of understanding what a rate means than the percentage itself. The same applies to debt growing at a fixed rate.
What is the equivalent for tripling?
Divide 114 by the rate; for ten-fold growth, divide 240. Both come from the same logarithm with a different target, and both are shown above so you do not have to remember them.
Does it work with regular contributions?
No. The rule describes a single sum compounding on its own. Adding money each month changes the shape entirely and needs a compound interest calculation with contributions, not a doubling-time shortcut.

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