Rule of 72 Calculator
This Rule of 72 calculator estimates how long it takes for an investment to double in value at a given annual interest rate. Enter the rate and it instantly returns the approximate number of years needed to double your money, using nothing more than the well-known mental-math shortcut of dividing 72 by the rate. It is a quick way to gauge the power of compound growth without reaching for a spreadsheet, whether you are comparing savings accounts, evaluating an investment, or simply curious how fast money grows.
Years to double
years
The Rule of 72 is an approximation: divide 72 by the annual interest rate to estimate how many years an investment takes to double. It works best with rates between 6% and 10%; outside that range the estimate loses accuracy.
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How it works
The Rule of 72 divides the number 72 by the annual interest rate (as a whole percentage) to approximate the number of years it takes for an amount to double under compound interest. For example, at 8% the estimate is 72 ÷ 8 = 9 years, and at 6% it is 72 ÷ 6 = 12 years. The rule works because the exact doubling time is ln(2) ÷ ln(1 + r), and 72 happens to be a convenient, easily divisible number that closely matches that math for typical rates. It is most accurate for annual rates between roughly 6% and 10%; for very high or very low rates the estimate drifts from the exact value, but it remains a fast and remarkably reliable rule of thumb.
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Preguntas frecuentes
- What is the Rule of 72?
- The Rule of 72 is a simple mental-math shortcut for estimating how long it takes an investment to double at a fixed annual compound interest rate. You divide 72 by the interest rate expressed as a whole number, and the result is the approximate number of years to double your money.
- How accurate is the Rule of 72?
- It is an approximation, not an exact figure. It is most accurate for annual rates between about 6% and 10%, where it comes within a fraction of a year of the true doubling time. For very high or very low rates it drifts a bit from the exact value calculated with logarithms, but it stays close enough to be a reliable quick estimate.
- Can you give an example?
- At an annual rate of 8%, the Rule of 72 gives 72 ÷ 8 = 9 years to double your money. At 6% it gives 72 ÷ 6 = 12 years, and at 9% it gives 72 ÷ 9 = 8 years. So a sum growing at 8% per year would roughly double in nine years.
- Why 72 and not another number?
- The exact doubling time is ln(2) ÷ ln(1 + r), which for small rates is close to 69.3 divided by the percentage rate. The number 72 is used instead because it is very close to that value and has many divisors (2, 3, 4, 6, 8, 9, 12…), making the mental arithmetic much easier.
- Can I use the Rule of 72 to find the required rate?
- Yes. Because the relationship is symmetric, you can also divide 72 by the number of years to estimate the rate needed to double in that time. For example, to double your money in 6 years you would need roughly 72 ÷ 6 = 12% per year.