Key Takeaways:
- The rule of 72 can help you forecast how long it will take for your investments to double.
- Divide 72 by the annual fixed interest rate to determine the rate at which the money would double.
- Historical returns on your investment type can help choose a realistic expected return rate, in some cases.
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 of time 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.
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
| Dividend | Annual Interest Rate | Investment Doubles in… | ||
| 72 | ÷ | 14% | = | 5.1 years |
| 72 | ÷ | 8% | = | 9 years |
| 72 | ÷ | 5.50% | = | 13.1 years |
| 72 | ÷ | 4% | = | 18 years |
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
| Dividend | Desired Years to Double Investment | Annual Interest Rate Needed Is… | ||
| 72 | ÷ | 4 | = | 18% |
| 72 | ÷ | 7 | = | 10.29% |
| 72 | ÷ | 11 | = | 6.55% |
| 72 | ÷ | 15 | = | 4.8% |
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
| Interest Rate | Difference From 8% | Adjusted Dividend | New Calculation | Investment Doubles in… | |
| 14% | 6 | 72 + 2 = 74 | 74÷ 14 | = | 5.29 years |
| 11% | 3 | 72 + 1 = 73 | 73÷ 11 | = | 6.64 years |
| 5% | -3 | 72 – 1 = 71 | 71÷ 5 | = | 14.2 years |
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.
The 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.
Investing Tips for Beginners
- If you’re new to investing, a financial advisor could help you create a financial plan for your needs and goals. Finding a financial advisor doesn’t have to be hard.SmartAsset’s free tool matches you with up to three vetted financial advisors who serve your area, and you can have free introductory calls with your advisor matches to decide which one you feel is right for you. If you’re ready to find an advisor who can help you achieve your financial goals, get started now.
- SmartAsset’s investment calculator can help you determine how your money will grow over time. This can be incredibly helpful to know as you plan out your and your family’s financial future.
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