Rule of 72 Calculator
ガイド
Rule of 72 Calculator
A fast, two-way doubling-time calculator. Enter an annual rate to see how many years money takes to double, or enter a target number of years to see the rate you need. The tool compares the classic mental-math shortcuts (Rule of 72, 70, and 69.3) against the exact compound result derived from logarithms, so you can see when each approximation is most accurate.
使用方法
- Pick a direction: Rate → Years (how long does it take to double?) or Years → Rate (what return do I need?).
- Enter the annual interest rate as a percent (e.g.
7for 7%) or the target doubling period in years. - Choose a compounding frequency. The exact-formula row updates accordingly; the 72/70/69.3 rows stay the same since they ignore compounding cadence.
- Optional: enter an inflation rate to see the real (purchasing-power) doubling time alongside the nominal result.
- Read the headline figure for a quick answer, and the comparison table to see which approximation is closest to the exact value at your rate.
機能
- 双方向 – Convert rate to doubling years, or doubling years to required rate, with one click.
- Three approximations side-by-side – Rule of 72, Rule of 70, and Rule of 69.3 in one comparison table.
- Exact compound math – Logarithmic solution shown alongside the rules of thumb so you can see the approximation error.
- Compounding frequency – Annual, semiannual, quarterly, monthly, daily, or continuous compounding.
- Real (inflation-adjusted) result – Subtract inflation to see how long until your purchasing power actually doubles.
- リアルタイム更新 – Numbers recalculate as you type, no submit button needed.
よくある質問
-
Where does the number 72 come from?
It is an approximation of 100 multiplied by the natural log of 2, which equals about 69.3147. The exact compound-growth formula for doubling time is ln(2) divided by ln(1 + r). For small rates this simplifies to about 0.693 divided by r. Because 72 has many small divisors (2, 3, 4, 6, 8, 9, 12) it makes mental arithmetic much easier than 69.3, and the small error it introduces is usually acceptable.
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When is the Rule of 72 most accurate?
The Rule of 72 is most accurate for annual returns between roughly 6 percent and 10 percent. At very low rates (below 4 percent), the Rule of 70 gives a closer answer. At higher rates (above 12 percent), all three rules under-estimate the true doubling time and the exact logarithmic formula should be preferred.
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How does compounding frequency affect doubling time?
More frequent compounding shortens the exact doubling time slightly because interest earned during the year starts earning interest itself. Continuous compounding produces the shortest doubling time for a given nominal rate. The Rule of 72 approximation does not account for compounding frequency, which is one reason the exact-formula row in the comparison table can diverge from the rules of thumb.
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What is the difference between nominal and real doubling time?
Nominal doubling time uses the stated interest rate. Real doubling time subtracts inflation first, so it tells you how long until your money doubles in purchasing power. If inflation equals or exceeds the nominal rate, real purchasing power never doubles, no matter how long you wait.
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Can the Rule of 72 be used for things other than money?
Yes. Any quantity that grows at a constant percentage rate per period can use the same approximation: population growth, bacterial cultures, GDP, debt, even depreciation by analogy. The math is identical because it depends only on exponential growth, not on what the quantity represents.
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