The Rule of 72: How to Estimate When Your Money Doubles

How long will it take your investment to double? The Rule of 72 gives you a surprisingly accurate answer in seconds — no calculator needed.

The Rule of 72 is a simple estimation formula: divide 72 by the annual interest rate (as a whole number), and the result is approximately how many years it takes for your investment to double. At 6% annual returns, your money doubles in about 72 ÷ 6 = 12 years. At 8%, it doubles in roughly 72 ÷ 8 = 9 years. At 12%, just 72 ÷ 12 = 6 years.

This mental shortcut has been in use for over 500 years. The Italian mathematician Luca Pacioli described a version of the rule in his 1494 work Summa de Arithmetica, making it one of the oldest financial rules of thumb still in use today (source: sec.gov/investor/pubs).

The mathematical basis for the Rule of 72 comes from the compound interest formula A = P(1 + r)^t. To find when A = 2P (doubling), we solve: 2 = (1 + r)^t, which gives t = ln(2) / ln(1 + r). For small values of r, ln(1 + r) ≈ r, so t ≈ ln(2) / r ≈ 0.6931 / r. Multiplying both sides by 100 gives t ≈ 69.31 / (r × 100). The number 72 is used instead of 69.31 because it has more factors (making mental division easier) and provides slightly better accuracy for typical interest rates between 4% and 12%.

Let us compare the Rule of 72 estimates to actual doubling times using the compound interest formula:

At 2%: Rule of 72 says 36 years. Actual: 35.0 years. Error: +2.9% At 4%: Rule of 72 says 18 years. Actual: 17.67 years. Error: +1.9% At 6%: Rule of 72 says 12 years. Actual: 11.90 years. Error: +0.8% At 8%: Rule of 72 says 9 years. Actual: 9.01 years. Error: -0.1% At 10%: Rule of 72 says 7.2 years. Actual: 7.27 years. Error: -1.0% At 12%: Rule of 72 says 6 years. Actual: 6.12 years. Error: -2.0%

The rule is most accurate around 8% interest — which happens to be close to the historical average annual return of the S&P 500 (approximately 10.3% nominal, 7.1% after inflation, according to data from NYU Stern's Damodaran database, source: pages.stern.nyu.edu/~adamodar).

You can also use the Rule of 72 in reverse. If you want your money to double in a specific number of years, divide 72 by the number of years to find the required interest rate. Want to double your money in 10 years? You need approximately 72 ÷ 10 = 7.2% annual returns. In 5 years? You need about 72 ÷ 5 = 14.4%.

The Rule of 72 also works for understanding inflation. According to the Bureau of Labor Statistics, the average annual inflation rate in the United States from 1990 to 2025 was approximately 2.8% (source: bls.gov/cpi). At 2.8% inflation, the purchasing power of a dollar halves in about 72 ÷ 2.8 = 25.7 years. This means $100 today will buy only about $50 worth of goods in 26 years.

You can apply the rule to other growth rates too. If your salary grows at 3% per year, it will double in about 72 ÷ 3 = 24 years. If a country's GDP grows at 5%, it doubles in 72 ÷ 5 = 14.4 years.

The rule has some well-known limitations. First, it works best for interest rates between 2% and 12%. Below 2% or above 12%, the error increases. For very high rates, the Rule of 69 or Rule of 70 may be more accurate. Second, the rule assumes annual compounding. With more frequent compounding, the actual doubling time is slightly shorter than the Rule of 72 predicts. Third, it only estimates the first doubling. To estimate when your money will quadruple, simply double the time (it takes two doubling periods). To reach eight times your original amount, triple the time.

The Rule of 72 becomes especially powerful when comparing investment options. Consider two funds: Fund A returns 6% and Fund B returns 9%. With the Rule of 72, Fund A doubles your money in 12 years while Fund B doubles it in 8 years. Over 24 years, Fund A doubles twice (4x), while Fund B doubles three times (8x). The 3-percentage-point difference in annual returns leads to a 2x difference in total wealth over 24 years.

According to the Federal Reserve Economic Data (FRED), the average annual return on 10-year Treasury bonds from 1962 to 2025 was approximately 5.8% (source: fred.stlouisfed.org). At that rate, money invested in Treasuries doubles in about 72 ÷ 5.8 = 12.4 years. By contrast, the S&P 500's nominal average of about 10% doubles money in just 7.2 years.

To see the Rule of 72 in action with your own numbers, use the CalcMyCompound calculator. Enter your principal amount, set the interest rate, and check the year-by-year table to find exactly when your investment first exceeds double the original amount. You can compare different rates side by side to see how compounding transforms small rate differences into large wealth differences.

Key takeaways: Divide 72 by the interest rate to estimate doubling time. Most accurate between 4-12% interest rates. Works in reverse — divide 72 by desired years to find the required rate. Also useful for estimating inflation impact on purchasing power.