Rule of 72 Calculator (Investment Doubling Time)
Estimate how long it will take for your investment capital to double in value at a fixed rate of return. This calculator compares the historic mental math Rule of 72 approximation against exact logarithmic continuous compounding equations.
Anticipated steady annual rate of return or yield
Starting amount committed to investment asset
Approximate years to double: 72 ÷ Interest Rate
How to Use This Calculator
- Enter your expected annual compound interest or stock market return rate.
- Enter your initial starting principal deposit.
- Compare the classic Rule of 72 estimate with the exact mathematical figure.
- Multiply doubling cycles across your long-term retirement timeline (e.g., 2 doublings = 4x capital).
Formula & Calculation Methodology
The Rule of 72 leverages the natural logarithm of 2 (~0.693), rounded to 72 for convenient divisibility across integers 2, 3, 4, 6, 8, 9, and 12.
Worked Example
$10,000 invested in broad equity market index at 8% annual return
Frequently Asked Questions
Why is the number 72 chosen instead of 69 or 70?↓
Mathematically, continuous compounding uses ln(2) ≈ 69.3%. However, 72 is preferred for mental arithmetic because it has numerous convenient integer divisors: 2, 3, 4, 6, 8, 9, and 12.
At what interest rates is the Rule of 72 most accurate?↓
The rule is remarkably accurate between 6% and 10%. At 8%, the rule predicts 9.00 years compared to the exact 9.01 years—a margin of error under 0.1%.
What should I use for very high growth rates (like 20% or 30%)?↓
For returns above 15%, the Rule of 72 begins to underestimate time slightly. Financial mathematicians often use the Rule of 73 or 74 for rates exceeding 20%, or rely on exact logarithmic formulas.
Can the Rule of 72 be used to calculate inflation’s purchasing power halving?↓
Yes. Dividing 72 by the annual inflation rate tells you how many years until the purchasing power of your cash is halved (e.g., at 3% inflation, money loses half its value in ~24 years).
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Open calculator →Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.