Why does the rule of 72 use 72?

The exact doubling time is ln 2 ÷ ln(1 + r), and ln 2 is about 0.693, so the mathematically pure constant would be near 69.3 for continuous compounding. Seventy-two is preferred because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and because the small upward adjustment happens to compensate for annual rather than continuous compounding across the rates people actually use. It is accurate to within a few months between about 4 % and 12 %, and drifts noticeably outside that band.

Should I use nominal or real growth?

Real, if the point of the exercise is what the money will buy. Growing 10,000 at 7 % while prices rise 3 % leaves about 3.9 % of real growth a year — the ratio 1.07 ÷ 1.03, not the subtraction — and after ten years that is 14,637 in today's purchasing power rather than 19,671. Nominal figures are the right ones only when the obligation itself is nominal, such as a fixed loan repayment that inflation quietly shrinks.

Seven Per Cent for Ten Years Almost Exactly Doubles

Published 9/24/2026 · 3 min read · Finance calculators

Camille Laurent — Finance writer at OneKitly

Tax · Personal finance

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In short

Compound growth multiplies rather than adds: 10,000 at 7 % a year for ten years is 10,000 × 1.07¹⁰ = 19,671.51, a rise of 96.7 % rather than the 70 % that ten annual additions of 700 would give. The extra 26.7 points are the growth on the growth, and they arrive almost entirely in the second half of the period — years one to five add 4,025, years six to ten add 5,646. This is also why the rule of 72 works: 72 ÷ 7 = 10.3 years to double, and the calculation says the doubling really happens a few months past year ten. The same arithmetic runs in both directions, which is why a 7 % annual price rise doubles a cost over a decade just as reliably as it doubles a savings pot.

10,000 growing at 7 % a year becomes 19,671.51 after ten years — a rise of 96.7 %. The rule of 72 predicted 10.3 years to double, and it was right to within four months.

An average of two annual rates is not the growth rate

Gain 50 % one year and lose 50 % the next and the arithmetic mean is zero, while the money is down 25 %: 1.5 × 0.5 = 0.75. Compound growth uses the geometric mean, which for that pair is −13.4 % a year, and the difference between the two means is not a rounding detail — it is the reason a volatile investment quoted by its average annual return can be losing money the whole time. Whenever growth is chained across periods, only the geometric figure describes what happened.

Two points of fees eat a third of the gain

Run the same ten years at 5 % instead of 7 % and 10,000 becomes 16,288.95: the gain falls from 9,671.51 to 6,288.95, so two percentage points of annual cost removed 35 % of the profit. This is the strongest argument in personal finance and it needs no forecast to be true, because the fee is certain while the return is not. Lengthen the horizon and it gets worse — over thirty years the same two points take away more than half.

10,000 at 7 %, where the growth actually lands
Period	Value at end	Added in period
Years 1–5	14,025.52	4,025.52
Years 6–10	19,671.51	5,646.00

Worked with our own calculator

Compound growth calculator

Given

Initial value: $20,000.00
Growth rate per period (%): 8.8
Number of periods: 20

Result

Final value: $108,045.80
Total gain: $88,045.80
Overall growth: 440.23%

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

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Frequently asked questions

Why does the rule of 72 use 72?: The exact doubling time is ln 2 ÷ ln(1 + r), and ln 2 is about 0.693, so the mathematically pure constant would be near 69.3 for continuous compounding. Seventy-two is preferred because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and because the small upward adjustment happens to compensate for annual rather than continuous compounding across the rates people actually use. It is accurate to within a few months between about 4 % and 12 %, and drifts noticeably outside that band.
Should I use nominal or real growth?: Real, if the point of the exercise is what the money will buy. Growing 10,000 at 7 % while prices rise 3 % leaves about 3.9 % of real growth a year — the ratio 1.07 ÷ 1.03, not the subtraction — and after ten years that is 14,637 in today's purchasing power rather than 19,671. Nominal figures are the right ones only when the obligation itself is nominal, such as a fixed loan repayment that inflation quietly shrinks.

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