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The Rule of 72: Why This One Number Predicts How Fast Money Doubles

The math behind the Rule of 72, why 72 was chosen over the more 'correct' 69.3, and exactly how accurate it is across real Indian interest rates.

Divide 72 by any annual interest rate, and you get, almost exactly, the number of years it takes for money growing at that rate to double. No calculator, no formula-typing — just mental division. It’s one of the oldest tricks in finance, and it’s genuinely accurate enough to plan around.

💡 Try it right now

PPF currently pays 7.1%. 72 ÷ 7.1 ≈ 10.1 years. Run the exact number through the PPF Calculator and you'll find the real answer is 10.11 years — the mental-math version was off by about 5 days.

Where the number comes from

Compound growth follows the formula A = P × (1 + r)ⁿ, where n is the number of years. Money doubles when A = 2P, so we need to solve (1 + r)ⁿ = 2 for n. Using logarithms, that works out to:

n = ln(2) / ln(1 + r)  ≈  0.693 / r  (for small r)

ln(2) ≈ 0.693, so multiplying by 100 to work in whole percentages gives 69.3 — that’s the mathematically “true” constant for continuous compounding. If 69.3 is more accurate, why does everyone use 72?

Why 72, not 69.3 (or 70)

Two reasons, and they trade off against each other:

1. Divisibility. 72 has far more whole-number divisors than 69 or 70 — you can divide it cleanly by 1, 2, 3, 4, 6, 8, 9 and 12. That means “72 ÷ rate” is easy to do in your head for almost any common rate, while 69.3 forces you to reach for a calculator anyway, defeating the purpose of a mental-math shortcut.

2. Accuracy where it matters. 72 isn’t just “close enough” — it happens to be most accurate in roughly the 6–9% range, which is exactly where typical Indian debt instruments (FD, PPF, NSC) sit. That’s not a coincidence historically (the rule predates modern low interest-rate environments), but it is a happy one for Indian savers today.

Rule of 72 estimate vs. the precise doubling time, across interest rates A line chart comparing years to double money as estimated by the Rule of 72 against the mathematically precise figure, across rates from 2% to 30%. The two lines nearly overlap between roughly 6% and 12%, and separate slightly at very low or very high rates. Precise Rule of 72 2% 8% 12% 30% 36 yr
The two lines are almost indistinguishable between 6% and 12% — the two curves cross around 8%, where the Rule of 72 is accurate to within days.

Exactly how accurate is it?

RateRule of 72 saysPrecise answerOff by
2%36.0 years35.00 years+12.0 months
6%12.0 years11.90 years+1.3 months
7.1% (PPF)10.14 years10.11 years+0.4 months
8.1% (top bank FD)8.89 years8.90 years~0
12% (SIP assumption)6.00 years6.12 years−1.4 months
20%3.60 years3.80 years−2.4 months
30%2.40 years2.64 years−2.9 months

The pattern is clear: the Rule of 72 overestimates slightly at low rates, underestimates slightly at high rates, and is nearly perfect right in the middle — which happens to be where most guaranteed Indian savings instruments live. See these numbers applied to real instruments in How to Double Your Money.

The lesser-known variants

The same trick works for other multiples, just with a different numerator:

RuleEstimatesFormula
Rule of 70Doubling time, more accurate at low rates70 / rate
Rule of 72Doubling time, best divisibility + accuracy in the 6–9% range72 / rate
Rule of 114Tripling time114 / rate
Rule of 144Quadrupling time (two doublings)144 / rate

Rule of 144 is really just the Rule of 72 applied twice — 144 = 72 × 2 — which lines up with the “each doubling repeats” idea explored in How to Double Your Money.

Where it breaks down

The Rule of 72 assumes a constant annual rate with no withdrawals — real investments rarely behave that smoothly:

  • Market-linked returns (SIPs, equity funds) don’t grow at a fixed rate every year — the Rule of 72 estimate is only as good as the average return assumption you feed it. See the SIP Calculator for a year-by-year model instead.
  • Very high rates (above ~20%) see the gap widen to a few months — still directionally useful, but don’t rely on it for precision.
  • Very low rates (below ~4%) — like a plain savings account — overestimate slightly, meaning your money actually doubles a bit faster than the rule suggests, not slower.

For an exact answer at any rate or tenure, use the Compounding Calculator — the Rule of 72 is for the mental-math moment when you don’t have it open. And if you want to see why repeated doublings are sometimes called the eighth wonder of the world, that’s the natural next read.

Learn more from official sources

This is general information, not financial advice. Investment returns are not guaranteed.

Not financial advice. These tools are for informational purposes only. See how we calculate and our full disclaimer. · Last reviewed: 21 Jul 2026

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