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Rule of 72
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Rule of 72 Estimate
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Exact Doubling Time
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Doubled Amount
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Tripled In
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How the Rule of 72 Works
Years to Double ≈ 72 / Annual Rate (%)
Exact: Years = ln(2) / ln(1 + r) = 0.6931 / ln(1 + r)
For continuous compounding: Years ≈ 69.3 / Rate
The Rule of 72 works because 72 is close to 100 × ln(2) ≈ 69.3. For rates between 2% and 25%, the approximation error is less than 3%.
Quick Reference
Frequently Asked Questions
72 is a convenient approximation of 100 × ln(2) ≈ 69.3. The number 72 was chosen because it's divisible by many common interest rates (1, 2, 3, 4, 6, 8, 9, 12) making mental math easy. For continuous compounding, 69.3 is more accurate; for practical investing, 72 is close enough.
Yes — you can use it to see how long until inflation halves your purchasing power. At 3% inflation: 72 ÷ 3 = 24 years to lose half your purchasing power. At the Bank of Canada's 2% target: 72 ÷ 2 = 36 years.
⚠️ Assumes constant compounding. Real investment returns fluctuate year to year.
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