The Rule of 72
The Rule of 72 turns compound growth into mental arithmetic: divide 72 by the annual rate, and you have the years to double. It is the fastest way to feel what a rate means before any calculator gets involved — and knowing where it bends keeps it honest.
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The Table
| Annual rate | Rule of 72 says | Exact doubling time |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
Between 4% and 12% the rule lands within about 2% of the truth — better precision than any mental model deserves. The exact figure is ln(2) ÷ ln(1 + r), which is what the compound interest formula computes.
Why 72
The mathematically pure constant is 100 × ln(2) ≈ 69.3 — for continuous compounding, "Rule of 69.3" would be exact. 72 wins in practice for two reasons: annual compounding pushes the true constant slightly above 69.3 in the everyday rate range, and 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12. A shortcut you can actually do in your head beats a purer one you cannot.
Three Uses Beyond Savings
Inflation: at 3%, prices double — purchasing power halves — in about 24 years; that is the quiet argument against holding long-term savings in cash. Debt: a balance compounding at 18% doubles in about 4 years, which reframes minimum payments instantly. Required rate: inverted, 72 ÷ years gives the rate a goal demands — doubling in 6 years needs ~12%, a demanding assumption worth noticing. For any real decision, confirm the mental estimate in the compound interest calculator and read the input caveats in the calculator guide — steady-rate doubling is a model, and real returns vary.
Frequently Asked Questions
What is the Rule of 72?
A mental shortcut for compound doubling time: divide 72 by the annual growth rate in percent. At 8%, money
doubles in about 72 ÷ 8 = 9 years.
How accurate is the Rule of 72?
Within a few percent of the exact answer for rates between roughly 4% and 12%. At very low rates 69 or 70 is
closer; at high rates the rule increasingly underestimates the true doubling time.
Does the Rule of 72 work for inflation and debt?
Yes — any steady compound growth. At 3% inflation, prices double (purchasing power halves) in about 24 years;
a debt compounding at 18% doubles in about 4 years.