Rule of 72 Calculator
Instantly estimate how long it takes to double, triple, or quadruple your money at any interest rate — using the Rule of 72 shortcut alongside the exact logarithmic formula for comparison.
| Rate | Rule of 72 | Exact Years | Triple (114) | 4× (144) |
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What Is the Rule of 72?
The Rule of 72 is a simple mental math formula that estimates how long it takes to double a sum of money at a given fixed annual rate of return. Divide 72 by the annual interest rate percentage, and the result is approximately the number of years needed for the investment to double. At 6% per year, for example, 72 ÷ 6 = 12 years to double.
The rule works because of the mathematics of exponential growth. The exact doubling time is ln(2) / ln(1 + r), where ln is the natural logarithm. Since ln(2) ≈ 0.693, and multiplying by 100 gives roughly 69.3, the number 72 is used instead because it has more integer factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making mental division easier. The U.S. Securities and Exchange Commission (SEC) cites the Rule of 72 in its investor education materials as a fundamental compound interest concept.
Rule of 72 vs. Rule of 69.3 vs. Exact Formula
There are three ways to estimate doubling time, each with a different trade-off between simplicity and accuracy:
- Rule of 72 (annual compounding): 72 ÷ rate. Best for mental math and annual or periodic compounding. Error is under 0.2 years for rates between 6% and 10%.
- Rule of 69.3 (continuous compounding): 69.3 ÷ rate. Theoretically exact for continuously compounded interest (as used in some derivatives or bond pricing formulas). Less practical for everyday savings and investments.
- Exact formula: ln(2) / ln(1 + r). This is always precise regardless of the compounding frequency. Use it when precision matters — for example, when projecting retirement account balances over 30+ years.
According to Federal Reserve research on household wealth accumulation, the compounding gap between a 6% and 8% return is deceptively large over 30 years — a difference of just 2 percentage points roughly halves the doubling periods required. Understanding Rule of 72 intuitively helps savers grasp why a 1–2% fee drag on investments is so costly over decades.
Rule of 114 and Rule of 144 — Triple and Quadruple
The Rule of 72 extends naturally to other multiples:
- Rule of 114: Divide 114 by the annual rate to estimate years to triple your money. At 6%, that is 114 ÷ 6 = 19 years. The exact figure is ln(3) / ln(1 + r) ≈ 18.9 years.
- Rule of 144: Divide 144 by the rate to estimate years to quadruple your money. At 6%, 144 ÷ 6 = 24 years. The exact figure is ln(4) / ln(1 + r), which equals two doubling periods — at 6%, about 24 years.
These rules are useful for projecting long-term wealth milestones. A 30-year-old investor earning 7% real returns could see their portfolio grow to 4× its starting value by age 54 (144 ÷ 7 ≈ 20.6 years) — entirely through compound growth, with no additional contributions. Last updated: May 2026.
Practical Applications of the Rule of 72
The Rule of 72 applies equally to growth and to erosion of value:
- Investments: A diversified index fund returning 10% annually doubles roughly every 7.2 years. Over 30 years, that is approximately four doublings — turning $10,000 into $160,000.
- Debt: Credit card balances at 20% APR double in just 3.6 years if left unpaid. The SEC highlights this in its investor alerts as a major driver of household financial stress.
- Inflation: At 3% annual inflation, purchasing power is halved in 24 years — meaning $100 today buys roughly $50 worth of goods by 2050. The Federal Reserve targets 2% inflation; at that rate, purchasing power halves in 36 years.
- Economic growth: An economy growing at 3% per year doubles its GDP in 24 years. China's rapid growth at 7–10% in the 2000s was compressing its doubling period to just 7–10 years.