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How Long Does It Take to Double Your Money?

The rule of 72 answers it in your head, and it is accurate enough to be useful. Where it comes from, where it drifts, and what it quietly assumes.

· 2 min read

Divide 72 by the annual growth rate and you have the number of years it takes to double. At seven percent that is about ten years; at nine percent, eight. The arithmetic is simple enough to do while someone is still talking, and it is close enough to right that the exact answer rarely changes the decision.

Where the 72 comes from

Doubling under compounding is a logarithm problem: the exact answer is the natural log of two divided by the log of one plus the rate. The natural log of two is about 0.693, which is where 69.3 would come from. The number is nudged up to 72 because it divides cleanly by so many small integers, and because that nudge happens to improve accuracy in the range people actually use.

rate   rule of 72   actual
 4%     18.0 yrs     17.7
 8%      9.0 yrs      9.0
12%      6.0 yrs      6.1
20%      3.6 yrs      3.8

The rule is at its most accurate around eight percent and drifts either side. At very low rates it slightly understates the time, and above about fifteen percent it understates it more noticeably. For anything in the range a savings account or a broad index fund realistically produces, the error is well inside the uncertainty of the rate itself.

What the rule quietly assumes

It assumes a single lump sum, left alone, growing at a constant rate. Real saving rarely looks like that. Regular contributions change the picture entirely, because each one starts its own compounding clock, and a portfolio that averages seven percent over a decade almost certainly did not return seven percent in any individual year.

The rule tells you what a rate does to money. It does not tell you what a market does to a rate.

Run it backwards for inflation

The same arithmetic works on the way down. At three percent inflation, 72 divided by 3 says prices double in roughly twenty-four years, which is another way of saying money left in cash loses half its purchasing power over that period. Subtracting inflation from your growth rate before applying the rule gives the doubling time in real terms, which is the number that actually matters.

Why the last doubling is the big one

Each doubling adds as much as every previous one combined. A balance that doubles five times has grown thirty-twofold, and the fifth doubling alone accounts for half of the final figure. This is why compounding feels slow for years and then suddenly does not, and why time in the market tends to matter more than the precise rate.

  • Doubling time depends on the rate, not on the amount — a small balance doubles as fast as a large one.
  • Contributions do not appear in the rule at all; model them separately.
  • Use the real rate, after inflation, if you want the answer in today’s money.

Frequently asked questions

Why 72 rather than 69 or 70?
Because 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the mental arithmetic easy. It also happens to be slightly more accurate than 69.3 across the mid single-digit rates people most often use.
Does the rule work for monthly compounding?
Closely enough. More frequent compounding shortens the doubling time a little, but at typical rates the difference is a fraction of a year — smaller than the uncertainty in the rate you assumed.
Does it apply to debt as well as savings?
Yes, and unpleasantly so. An unpaid balance at eighteen percent doubles in about four years, which is why compounding works exactly as hard against a borrower as it does for a saver.

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