Dennis Hammer is a writer and finance nerd with six years of investing experience. He writes about personal finance for sahib.tv. Dennis also manages his own investment portfolio and has funded several businesses in the past. Dennis holds a Bachelor's degree from the University of Connecticut.
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It’s hard to determine whether a stock, bond, or other security is a good buy without knowing how much you can earn from holding it. But if you aren’t comfortable with math, you probably find it tedious and painful to slog through equations whenever you consider an investment.
Well, you’re in luck! The Rule of 72 is a quick way to compare stocks and bonds without stressing over the math.
What is the Rule of 72?
What's the Rule of 72?
The Rule of 72 is an easy way to estimate how long before an investment doubles. Simply divide the interest rate by 72 to determine the number of years it will take to double.
The Rule of 72 is an easy way to estimate how long it will take for an investment to double, given a fixed annual interest rate. By dividing 72 by the annual rate of return, you can get a rough estimate of the number of years it will take to double your initial investment.
This rule is a quick way to understand the impact of compound interest. Compound interest is the principle by which the interest you earn also earns interest. It’s an important investment concept, and it’s why you should continually reinvest your earnings. Notice how much more you can earn by holding investments that compound as opposed to those that don’t.
Compound interest is not easy to calculate, especially if you’re trying to do math in your head. If you earned 5% compounding interest on $1,000, you would earn $50 the first year, $52.50 the second year (which is 5% of $1,050), $55.13 the third year (which is 5% of $1,102.50), etc. The first step is easy to figure out on your own, but the rest requires a table or a complex formula.
Yes, there are countless calculators, equations, and Excel sheets that will help you determine how much you’ll earn from an investment, but the Rule of 72 is a handy mental method to gauge the investment’s approximate value. It’s perfect for some quick “napkin math” before you dive into some deeper analysis.
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The Rule of 72 also creates a simple standard for comparing investments against one another. You could apply the rule to two different investments to learn which one will double in the shortest amount of time. The one that doubles first would earn the most in the long run.
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Origin of the Rule of 72
The concept of interest has been around since ancient Mesopotamian, Greek, and Roman civilizations. It’s also mentioned in the Quran. It was primarily used in agriculture and land transactions, as well as standard money loans. Lenders have always needed to know how much they’ll earn from an investment.
The first reference we have of the Rule of 72 comes from Luca Pacioli, a renowned Italian mathematician. He mentions the rule in his 1494 book Summa de arithmetica, geometria, proportioni et proportionalita (“Summary of Arithmetic, Geometry, Proportions, and Proportionality”). Here’s what Pacioli says about it:
In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule
As you can see, Pacioli presents the rule in a discussion about the timeframes of doubling investments, but he doesn’t derive or explain it. We assume the rule was invented by someone else. Paciolio is just the first to mention it in a published work. Some people credit Albert Einstein for inventing the rule, but there’s no evidence to support this.
Other applications
The Rule of 72 can be used to calculate the growth of anything that’s subject to compound interest, as long as you know the rate of growth.
A country’s GDP, for example, typically increases at a compound rate. If we know the rate of growth, we can use the Rule of 72 to figure out how long it will take to double. Let’s say a country’s GDP grows at 4%. 72/4 = 18, so it would take 18 years for the GDP to double at that rate. The length of time could change, of course, if the rate of growth changes.
Inflation is another value we can look at with the Rule of 72. If money inflates at 3%, we know it will take 24 years before its value doubles. This might help you decide to invest (or not invest) in a foreign currency or foreign bond.
In fact, we can use the Rule of 72 to look at more than just financial concepts. We can estimate when anything will double if we know the growth rate. For instance, you could predict when a population would double. If you know the population grows by 5%, it would double in 14.4 years.
Rule of 72 formula
Calculating the rule of 72 is remarkably simple. Unlike most investment equations, you don’t need to know a complex formula. In some cases, you can perform this calculation in your head.
The estimated number of years to double an investment = 72 / compound annual interest rate
Note: You must use the annual interest rate as a whole number, not a decimal (e.g., “5”).
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The Rule of 72 isn’t perfectly accurate, but it’s reasonably accurate for low rates of return. Since we’re doing quick-and-dirty math here, it’s accurate enough for our purposes. The following chart compares the results from the Rule of 72 versus the actual number of years it will take to double the investment.
