Plot No. 25 · Money & Finance
Rule of 72 Calculator
Estimate how many years it takes for money to double at a given annual interest rate by dividing 72 by the rate. It also shows the exact doubling time using logarithms, so you can see how close the shortcut lands, plus the rate needed to double in 10 years.
The Rule of 72 is a mental-maths shortcut, most accurate for rates between about 6% and 10%. The exact figure uses logarithms and assumes the rate compounds once a year.
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How the Rule of 72 is worked out
The Rule of 72 is a mental-maths shortcut for how long money takes to double. You simply divide 72 by the annual interest rate. At 7% that is 72 divided by 7, about 10.3 years. It works because the true doubling time involves logarithms, and over the common range of rates that maths comes out close to 72 divided by the rate.
The calculator also shows the exact doubling time, which is the natural log of 2 divided by the natural log of one plus the rate. The number 72 is chosen over the more precise 69.3 because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, making it easy to do in your head. The shortcut drifts a little at the extremes, slightly overestimating at high rates and reading nearer 69 or 70 at very low ones.
How to use the Rule of 72 calculator
- Enter the annual interest or growth rate as a percentage.
- Read the Rule of 72 estimate for years to double alongside the exact figure.
- Compare the two to see how close the shortcut lands, and note the rate needed to double in 10 years is 7.2%.
Worked examples
A typical rate
Inputs: 7% annual rate
Result: The Rule of 72 gives about 10.3 years to double, and the exact logarithmic figure is about 10.2 years, so the shortcut is within a couple of months.
A high rate where it drifts
Inputs: 24% annual rate
Result: The rule estimates 3.0 years, but the exact doubling time is about 3.2 years, showing the rule starts to underestimate the time at high rates.
Limitations and common mistakes
Edge cases and limitations
- It is an approximation, most accurate for rates between about 6% and 10%.
- The exact figure assumes the rate compounds once a year; more frequent compounding doubles money slightly faster.
- It needs a rate above zero, since a zero or negative rate never doubles.
Common mistakes
- Treating the Rule of 72 result as exact, when at high rates it can be off by several months.
- Forgetting that the rule assumes a constant rate every year, which real investments rarely deliver.
Frequently asked questions
How does the Rule of 72 work?
Divide 72 by your annual interest rate to estimate the number of years for money to double. At 7%, that is 72 divided by 7, which is about 10.3 years. The exact answer using logarithms is about 10.2 years, so the shortcut is very close.
Why is the number 72 used?
The true doubling time is the natural log of 2 divided by the log of one plus the rate. Multiplying that out gives roughly 69.3 divided by the rate at low rates, but 72 is used because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which makes mental maths easy.
When does the Rule of 72 become inaccurate?
It is most accurate around 6% to 10%. At very low rates the closer approximation is nearer 69 or 70, and at high rates above about 20% the rule starts to overestimate the doubling time. For everyday rates it stays within a few months of the exact figure.
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