Rule of 72
How many years for your money to double.
Years to double
9
Years to triple (rule of 114)
14.3
Years to quadruple (rule of 144)
18
How it works
The Rule of 72 is one of the most useful mental shortcuts in personal finance. Attributed to Luca Pacioli in the 15th century, it lets you estimate in your head how many years an investment takes to double at a given compound annual rate. Accuracy is surprisingly high for rates between 4% and 15% — exactly the range that matters for most real-world investments.
Formulas:
Years to double ≈ 72 / Rate% Years to triple ≈ 114 / Rate% Years to quadruple ≈ 144 / Rate%
Why does it work? Because of compound interest math: time = ln(2) / ln(1+r). Since ln(2) ≈ 0.693 and ln(1+r) ≈ r for small rates, the result is approximately 0.693/r. Multiplied by 100, that's ≈ 69.3/Rate%, but 72 is more convenient because it has many integer divisors (2, 3, 4, 6, 8, 9, 12).
Practical applications: at 8% per year (long-run S&P 500 average), your money doubles in 9 years. At 4% (typical bonds), 18 years. At 12% (high-growth equity), just 6 years. The rule also works in reverse for inflation: at 5% annual inflation, your money loses half its purchasing power in ~14 years.
Practical examples
8% annual rate
Doubles in 9 years · Triples in 14.3 years · Quadruples in 18 years
12% annual rate (historical equity returns)
Doubles in 6 years · Triples in 9.5 years · Quadruples in 12 years
4% annual rate (US Treasury bonds)
Doubles in 18 years · Triples in 28.5 years · Quadruples in 36 years
6% annual rate (moderate fixed income)
Doubles in 12 years · Triples in 19 years · Quadruples in 24 years
Frequently asked questions
Is the Rule of 72 exact?
It's a very good approximation between 4% and 15%. Accuracy drops at extremes. For 1%, the exact formula gives 69.7 years; the rule estimates 72. For 30%, exact = 2.64 years, rule = 2.4. For casual use, precision is more than enough.
Does it work for simple interest?
No. The Rule of 72 only applies to compound interest. With simple interest, doubling at 8% takes exactly 12.5 years (100/8), not 9.
Can I use it for inflation?
Yes — it's a great application. At 6% annual inflation, your money loses half its purchasing power in 12 years. That's why fixed income matching inflation doesn't build real wealth.
Why 72 and not 70 or 69?
70 and 69 also work (and 69 is actually more accurate at low rates). But 72 has many integer divisors (2, 3, 4, 6, 8, 9, 12), making mental math easier. It's a choice of convenience.
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