Rule of 72 Calculator

The Rule of 72 Calculator estimates how long it takes for an investment to double in value at a given annual rate of return. The rule is elegantly simple: divide 72 by the annual interest rate to get the approximate number of years to double your money. At 8% annual return, your money doubles in approximately 72 / 8 = 9 years.

The Rule of 72 is one of the most useful mental math shortcuts in finance. It provides a quick, reasonably accurate estimate without needing a calculator. The rule works because the exact doubling time formula — t = ln(2) / ln(1 + r) — produces values close to 72/r for interest rates in the 2-20% range. The number 72 was chosen because it has many factors (1, 2, 3, 4, 6, 8, 9, 12) making mental division easy.

The Rule of 72 is most accurate at rates around 8%, where it gives an exact result. At very low rates (1-2%), the Rule of 70 is more accurate. At very high rates (20%+), the Rule of 78 provides better estimates. For rates between 2% and 15%, the Rule of 72 typically has less than 2% error — precise enough for quick financial planning.

Beyond simple doubling, the Rule of 72 can be applied to various financial scenarios. It works for inflation erosion (at 3% inflation, purchasing power halves in 24 years), GDP growth (at 3% growth, an economy doubles in 24 years), population growth, and any exponential process. The rule can also work in reverse: if you know an investment doubled in 10 years, the annual return was approximately 72 / 10 = 7.2%.

Financial advisors use the Rule of 72 to quickly illustrate the power of compound interest to clients. Showing that $100,000 at 8% doubles to $200,000 in 9 years, $400,000 in 18 years, and $800,000 in 27 years makes the abstract concept of compounding tangible and motivating. This calculator shows both the Rule of 72 estimate and the exact mathematical result so you can see the approximation's accuracy.