#  ## Ron Harris

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## The Rule of 72 Explained

October 5, 2020

### In our book HowMoneyWorks: Stop Being a Sucker, we introduce the Rule of 72, a mental math shortcut for estimating the effect of any growth rate—from quick financial calculations to population estimates.

This formula is especially useful for financial estimates and understanding the nature of compound interest. Rates of return may not be the easiest subject for consumers since it isn’t taught in schools, but this simple rule can help show the significance of a percentage point here or time horizon there.

Here’s the formula: 72 ÷ Interest Rate = Years to Double. If you know the interest rate (or rate of appreciation) or the time in years, dividing 72 by that number will give you a good approximation of the unknown number.

When will your money double?* 72 ÷ 1% = 72 years to double 72 ÷ 3% = 24 years to double 72 ÷ 6% = 12 years to double 72 ÷ 9% = 8 years to double 72 ÷ 12% = 6 years to double

Here’s an example: If you’re receiving a 9% rate of return, just divide 72 by 9. The result is 8. That means your money will double in approximately 8 years. Maybe that’s not fast enough for you and you prefer your money to double every 5 years. Then simply divide 72 by 5. The result is 14.4. Now you know you need a 14.4% return to achieve your goal.

This rule, long known to accountants and bankers, provides a close idea of the time needed for capital to double.

If you think that a difference of 1% or 2% is insignificant—think again! You seriously underestimate the power of compound interest. If one account appreciates at 9% and another at 12%, the Rule of 72 tells you that the first will take 8 years to double while the second will need only six years. This formula is also useful for understanding the nature of compound interest.

Examples:*

• At 6% interest, your money takes 72 ÷ 6 = 12 years to double.
• To double your money in 10 years, you need an interest rate of 72 ÷ 10, or 7.2%.
• If inflation grows at 3% a year, the prices of things will double in 72 ÷ 3, or 24, years. If inflation slips to 2%, it will double in 36 years. If inflation increases to 4%, prices double in 18 years.
• If college tuition increases at 5% per year (which is faster than inflation), tuition costs will double in 72 ÷ 5, or about 14.4, years.
• If you pay 17% interest on your credit cards, the amount you owe will double in only 72 ÷ 17, or 4.2, years!

The Rule of 72 shows that a “small” 1% change can make a big difference over time. That small difference could mean buying the house you want, sending your kids to the college they choose, retiring when you wish, leaving your children the legacy they deserve, or settling for… something less. Doing the math with the Rule of 72 can give you critical insight to hit your goals down the road by shifting your strategy accordingly.

By the way, the Rule of 72 applies to any type of percentage, including something like population. Can you see why a population growth rate of 2% vs. 3% could be a huge problem for planning? Instead of needing to double your capacity in 36 years, you only have 24. Twelve years were shaved off your schedule with one percentage point faster growth.

The Rule of 72 was originally discovered by Italian mathematician Bartolomeo de Pacioli (1446-1517). Referring to compound interest, Professor Albert Einstein (1879-1955) is quoted as saying: “It’s the greatest mathematical discovery of all time.” He called it the 8th Wonder of the World—it works for you or against you. Make sure you put this shortcut to work the next time you consider an interest rate. When you save, it works for you. When you borrow, it works against you!

— Tom Mathews

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• The Rule of 72 is a mathematical concept that approximates the number of years it will take to double the principal at a constant rate of return compounded over time. All figures are for illustrative purposes only, and do not reflect the performance risks, fees, expenses or taxes associated with an actual investment. If these costs were reflected, the amounts shown would be lower and the time to double would be longer. The rate of return of investments fluctuates over time and, as a result, the actual time it will take an investment to double in value cannot be predicted with any certainty. Investing entails risk, including possible loss of principal. Results are rounded for illustrative purposes. Actual results in each case are slightly higher or lower.