The Rule of 72: What Is It, and How Can You Use It? (2024)

The rule of 72 is a simple formula that shows how quickly your money will double at a given return rate. It works by dividing 72 by your annual compound interest rate and seeing how many years it will take for your investment to double. There are many uses for the rule of 72, most notably planning ahead for your long-term investments and retirement goals. While it isn’t the most accurate way of projecting returns, it allows you to see if you’re keeping pace in a quick and basic way so that you can know if you’re on track.

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What Is the Rule of 72?

If you want to know how long it will take you to double your investment at a specific fixed interest rate, the rule of 72 is the fastest way to do so. But even if you’re not looking to multiply your money twofold, knowing the period it would take to do so can help you infer when you would reach your goal portfolio size.

Learning how to calculate compound interest is a complex mathematical procedure that leaves most people reaching for a calculator. To get started, figure out what your fixed compound annual interest rate is. Once you know this, you must divide it into 72 (hence the rule of 72). The quotient is the number of years it will take for your invested money to double in value.

When doing math, most people are used to writing out percentages in decimal forms, such as 4% written out as 0.04. Contrary to this, be sure to keep the rate as a whole number or your answer will be woefully off the mark.Below is a mathematical representation of the rule of 72:

72÷ your compound annual interest rate = how many years until your investment doubles

When it comes to the accuracy of this rule, the best results are found at an 8% annual interest rate. However, you can feel confident using it for any percentage from 4% to 15%. Beyond these parameters, the rule becomes a bit too imprecise to be trusted. In the end, though, nothing can beat doing a true compound interest calculation.

How You Can Use the Rule of 72

By dividing 72 by the annual interest rate, one can quickly determine the approximate number of years required for the investment to grow twofold. This rule is particularly useful for interest rates between 6% and 10%, offering a quick mental calculation for investors and financial planners alike. For higher precision, slight adjustments can be made depending on the specific interest rate, such as using 69 or 70 for very high or low rates.

In practical use, the Rule of 72 is valuable for a variety of financial scenarios. Investors can utilize it to estimate the growth of stocks, bonds, or savings accounts, allowing for better long-term financial planning. It also serves as a tool for understanding the impact of inflation on purchasing power, indicating how long it will take for money to lose half its value due to rising prices. Additionally, the rule is helpful for evaluating the compounding interest on debt, giving borrowers a clearer picture of how quickly their debt can grow if not managed properly.

Examples of How the Rule of 72 Formula Works

In this table, you’ll find a few examples of the rule of 72 in action:

The Rule of 72

The rule of 72 also works in reverse. You can divide the number 72 by the number of years in which you wish to double your investment, and the answer will show you the annual interest rate you need to achieve your goal. Look below to see a few scenarios where this could be helpful:

The Rule of 72: Reversed

Variations of the Rule of 72

Although the rule of 72 offers a fantastic level of simplicity, there are a few ways to make it more exact using straightforward math. Remember, an 8% interest rate is the most realistic simulation for the rule. For every three points that an interest rate strays from 8%, you can adjust “72” by one in the direction of the rate change. So if the rate is 5%, you would lower the rule to 71. On the other hand, a rate of 11% would result in a shift to 73, and a 14% rate would induce a 74.

The Rule of 72: Modified

What if the rule of 72 was actually titled the Rule of 69.3? Well for one, it wouldn’t roll off the tongue nearly as well. In actuality, though, utilizing the latter dividend has proven to offer better projections for those who take advantage of continuous compounding. This likely won’t add very much in terms of interest potential for an investment account. But it can make a small difference.

Banks have increasingly begun to employ daily compounding. This is most often found attached to savings accounts, money market accounts (MMAs) and certificates of deposit (CDs). All three of these account types are generally for long-term usage, so check to see if your bank includes them.

How the Rule of 72Came About

Interest has existed since ancient times in mathematical and economic studies. In fact, it appears to date as far back as the Mesopotamian, Roman and Greek civilizations. The Quran even makes mention of it. Its roots stem from agriculture and the first incarnations of land and money loans.

The first individual to mention the rule of 72, though, is Luca Pacioli, a renowned mathematician from Italy. His impressive book, “Summa de arithmetica, geometria, proportioni et proportionalita” (“Summary of Arithmetic, Geometry, Proportions and Proportionality”), was published in 1494 and holds the first known reference of the rule, making him the closest we know to an inventor. Some credit Albert Einstein as the architect of the rule. There is no documentation to support this claim, though.

Bottom Line

The rule of 72 can help you get a rough estimate of how long it will take you to double your money at a fixed annual interest rate. If you have an average rate of return and a current balance, you can project how long your investments will take to double. This is an incredibly useful tool for both retirement planning and long-term financial planning in general. Although you’ll also want to use a more in-depth projection method at some point, the rule of 72 can serve as a great starting point.

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