The Rule of 72: How Fast Will Your Money Double?
The Rule of 72 tells you how many years it takes money to double at a given rate: 72 ÷ rate. Learn why it works, its accuracy, and when to use variants.
There's exactly one piece of investing math you can do in your head at a dinner party, and this is it:
Years to double = 72 ÷ annual interest rate
At 6%, money doubles in about 12 years. At 8%, about 9 years. At 3%, about 24. That's it — the entire rule.
Why 72?
The exact doubling time under compound interest is:
t = ln(2) / ln(1 + r) ≈ 0.693 / r (for small r)
So the "true" number in the numerator is 100 × ln(2) ≈ 69.3, not 72. But 72 is chosen because it has more integer divisors (2, 3, 4, 6, 8, 9, 12) — you can do 72 ÷ 6 or 72 ÷ 8 in your head; 69.3 ÷ 6 you can't. The tiny loss in precision is worth the mental math.
Accuracy vs the exact formula
| Rate | Rule of 72 estimate | Exact doubling time | Error |
|---|---|---|---|
| 2% | 36.0 yr | 35.0 yr | +1.0 yr |
| 4% | 18.0 yr | 17.7 yr | +0.3 yr |
| 6% | 12.0 yr | 11.9 yr | +0.1 yr |
| 8% | 9.0 yr | 9.0 yr | 0.0 yr |
| 10% | 7.2 yr | 7.3 yr | −0.1 yr |
| 12% | 6.0 yr | 6.1 yr | −0.1 yr |
| 20% | 3.6 yr | 3.8 yr | −0.2 yr |
The rule is remarkably accurate between 4% and 12% — the range that covers most real-world returns and interest rates. At very low or very high rates, use the exact formula or the Compound Interest Calculator for precision.
Everyday applications
Investing. Stocks have returned roughly 7% real (after inflation) historically. 72 ÷ 7 ≈ 10 years to double in real purchasing power. Two doublings — twenty years — and $10,000 becomes $40,000 in today's dollars.
Inflation. Runs both ways. At 3% inflation, prices double in 24 years; your dollar's purchasing power halves in the same period. At 6% inflation (early 2020s territory), that collapses to 12 years.
Debt. A 24% APR credit card doubles the balance in 3 years if unpaid. That's why unpaid consumer debt spirals.
Savings account. At today's typical 4% high-yield savings rate: 18 years to double — barely keeping up with real inflation. The gap between "safe" and "invested" is exactly why the doubling-time perspective is useful.
For deeper mechanics on how compounding actually generates these doublings, see Compound Interest Formula Explained.
Variants for other multiples
- Rule of 69.3 — the mathematically exact version for continuous compounding. Better below 4%.
- Rule of 114 — years to *triple*. 114 ÷ rate.
- Rule of 144 — years to *quadruple* (which is just two doublings). 144 ÷ rate.
At 6%, money doubles in 12 years (72÷6), triples in 19 years (114÷6), and quadruples in 24 years (144÷6). Notice quadruple is exactly two doublings — 12 + 12 = 24 ✓.
A worked example
You have $20,000 to invest and want to know how big it will be at retirement in 36 years, assuming a 6% real return.
- Doublings = 36 ÷ 12 = 3
- Result = $20,000 × 2 × 2 × 2 = $160,000 in today's dollars
The exact answer at 6% for 36 years is $163,000 — the Rule of 72 nailed it within 2%.
FAQ
How does the Rule of 72 actually work? It's an approximation of the compound-interest doubling formula. The exact numerator is 100 × ln(2) ≈ 69.3, but 72 divides cleanly by more integers, making the mental math trivial at typical rates.
Is the Rule of 72 accurate? Very, between 4% and 12% — usually within 0.1–0.3 years of the exact answer. Below 4% use 69.3; well above 20% use the exact formula.
How long does it take to double your money at 5%? About 72 ÷ 5 = 14.4 years. The exact answer is 14.2 years — close enough for planning.
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*Turn the rule into a full projection: try the free Compound Interest Calculator for a year-by-year growth chart.*