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Rule of 72

For many, predicting how your investments will perform over the long term can be difficult. After all, these returns may often seem abstract and distant. But being able to determine a time frame for expected growth is invaluable. The rule of 72 does just this, so read on to learn exactly how to use this law. SmartAsset’s financial advisor matching tool can also set you up with a local advisor who can further aid you in evaluating your current investments or building an investment portfolio for the future.

The Rule of 72: What Is It?

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 form, 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 the Rule of 72

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

Some people may prefer to figure out what level of interest rate they need to double their investment. If this describes you, you can actually flip the divisor and quotient of the original rule of 72 to get your answer. 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

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 it.

Where Does the Rule of 72 Come From?

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.

Tips for Investing Newbies

Rule of 72

  • Financial advisors are constantly active in the investment sphere, giving them plenty of experience managing money and portfolios. The SmartAsset financial advisor matching tool pairs you up with as many as three professionals in your area. We choose them specifically for you according to your exact financial situation, needs and retirement dreams. So be as accurate as possible when going through the series of questions laid out to you.
  • Remembering to fund existing and new investments is tough. Many financial advisors, robo-advisors and other investing portals offer the ability to set up direct deposit. So just select how much to invest each month and let it do its thing.

Photo credit: ©iStock.com/lucky336, ©iStock.com/MicroStockHub, ©iStock.com/simonkr

Chris Thompson, CEPF® Chris Thompson is a retirement, savings, mortgage and credit card expert at SmartAsset. He has reviewed hundreds of credit cards and loves helping people find the one that best matches their financial needs. Chris is a Certified Educator in Personal Finance® (CEPF®) and a member of the Society for Advancing Business Editing and Writing. He graduated from Montclair State University where he received the Journalism Achievement Award. Chris’ articles have been featured in places like Yahoo Finance, MSN and Bleacher Report. He lives in New Jersey and is a Mets, Jets and Nets fan.
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