Rule of 72 Calculator

What is the Rule of 72?

The Rule of 72 is a quick and simple mathematical formula used to estimate how long it will take for an investment to double in value, given a fixed annual rate of return. By dividing 72 by the annual return rate, investors can get a rough estimate of the doubling time without doing complex logarithmic calculations.

For example, if you have an investment that returns 8% annually, the Rule of 72 suggests it will take approximately 9 years to double (72 / 8 = 9).

Rule of 72 vs. Rule of 70 vs. Rule of 69.3

While the Rule of 72 is the most famous, there are slightly more accurate variations depending on how the interest is compounded:

• Rule of 72: Best used for estimating general investment returns, especially those with annual compounding and rates around 6% to 10%. 72 is highly divisible, making mental math easy.
• Rule of 70: Often used for estimating the doubling time of inflation or population growth, or when interest rates are lower.
• Rule of 69.3: The most mathematically accurate estimate for continuous compounding, as the natural logarithm of 2 is approximately 0.693.

Why is Exact Time Different?

The rules of 72, 70, and 69.3 are all approximations designed for quick mental math. The exact time to double an investment is calculated using logarithms: t = ln(2) / ln(1 + r). As the interest rate increases, the estimates start to drift further away from the exact calculation. Our calculator computes both the exact time and the common estimates so you can see the differences firsthand.