What Is the Rule of 72?

The Rule of 72 is an easy, concise equation that calculates the amount of time your investment will need to increase its value twofold.

It's a reasonably accurate way to manually gauge an investment's growth rate or rate of return, which is an investment's net gain or loss over a specific period of time, without having to rely on elaborate software, complicated algebra, or other logarithmic calculating tools.

The Rule of 72 yields the most accurate results when interest rates are low, usually between 6 and 10 percent. The formula gives the most precise answers when the rate of return is 8 percent.

How does the Rule of 72 work?

Using the Rule of 72 is simple. Essentially all you need is one piece of information: the expected annual growth rate of your investment, which is also sometimes referred to as "rate of return" or "RoR."

Here's how the equation works: divide the number 72 by the expected annual growth rate. This determines the number of years it will take for your investment to double.

For example, if you invest $1,000 and the growth rate is 8 percent, all you have to do is divide 72 by eight, which is nine. That's to say, it will take approximately nine years for your $1,000 investment to become $2,000.

Let's say you invest $60,000 in a friend's doggy daycare startup or a loved one's new cafe. If the expected annual growth rate of your investment is 10 percent – which is interest that the borrower pays the lender – using the Rule of 72 lets you know that it will take slightly more than seven years – 7.2 years, precisely – for your $60,000 investment to become $120,000. Doing the math, 72 divided by 10 is 7.2.

If the expected annual rate of return is 2 percent, however, it would take approximately 36 years for your investment to double.

Simply put, the higher the annual growth rate of the investment, the quicker the profit.

That may seem pretty obvious, even if you're no math wiz. A steeper rate of return equals a faster return. What's particularly useful about the Rule of 72 is that it allows you to determine just how much time it will take for your investment to come full circle. That, in turn, helps you to decide whether a particular investment opportunity is savvy or a financial Pandora's box that's better of which to steer clear.

Why is the Rule of 72 used?

Essentially, the Rule of 72 can apply to anything that grows at a compounded interest rate or a rate that is based on the initial amount of investment.

In the financial world, experts use the Rule of 72 to determine the monetary return on anything that grows exponentially, such as a loan. Economists also use it to anticipate the growth rate of a country's gross domestic product or its national currency's inflation.

When it comes to lending capital, the Rule of 72 helps assess the overall impact that annual fees will have on your investment's growth over the life of the loan. 

The Rule of 72 also serves a purpose beyond banking and investing. Social scientists use it to determine population growth rates, whether locally, nationally, internationally, or globally. 

For example, if a city's population is 1 million residents and it has an annual growth rate of 7 percent, using the Rule of 72 you can calculate that it will take approximately 10.28 years for the population to reach 2 million. That is, as long as the annual growth rate remains the same. If it rises or falls, the time it takes for the population to grow to 2 million could be shorter or longer.

Who invented the Rule of 72?

The concept of interest, in general, has been around since Mesopotamian times – 6,000-7,000 years ago – when humans began to develop more complex ways of managing newfound agricultural-based economic systems by way of land and money loans.

As far as the first known mention of the Rule of 72 goes, Italian mathematician Luca Pacioli explained the theory in his 1494 book "Summary of Arithmetic, Geometry, Proportions, and Proportionality."

Thanks to Pacioli's reference, historians and mathematicians alike generally consider him the father of the Rule of 72.

Why is it called the Rule of 72?

So, what's so special about the number 72 when it comes to figuring out how long it will take to double your money invested? It's no magic. It's just simple math.

The actual formula to determine the precise amount of time it would take for an investment to double is a bit more complicated, to say the least: ln(2) / ln(1 + (interest rate/100)), with "ln" representing natural log value as it would on a calculator.

To gauge an even more precise estimate, investors will sometimes stray from the Rule of 72 by substituting a slightly different number as the dividend, such as 70 or 69.

This is because the exact number to find the most accurate return time on your investment is 69.3, not 72. But since 69.3 isn't exactly the easiest number to divide by without the help of a calculator, you can substitute it for another nearby number which is. Many more numbers yield even results when divided into, let's say, 70: the numbers 1, 2, 5, 7, and 10.

In fact, if you enter ln(2) on a calculator, the result is .69314718056. Or, after moving the decimal two spots to the right, 69.3.

Investors use the number 72 because several numbers divide evenly with it, including the numbers 1, 2, 3, 4, 6, 8, 9, and 12. This allows for a quick, easy, and reasonably accurate assessment of the amount of time it will take an investment to double with a wide range of growth rate percentages.

Given that it's simple, easy, and reliable, it's no surprise why the Rule of 72 is such a go-to lifesaver in the fast-paced world of finance.

Whether you're looking to invest a little or a lot, knowing how to apply the Rule of 72 will help you anticipate exactly how long it will take until you see your profits come rolling in.‍