# Application of the Rule of 72

###### Bottom Line

The Rule of 72 is a way to figure out how long it will take for your money to double at a certain rate of return. If your account makes 4%, for example, divide 72 by 4% to find out how long it will take for your money to double. 18 years in this case.

The same formula can also be used to figure out how long it will take for the original amount to drop in half instead of doubling.

The Rule of 72 is based on a more complicated calculation and is only an estimate, so it isn’t always right. The Rule of 72 is most accurate when it is based on an interest rate of 8%. The further away from 8% you go in either direction, the less accurate the results will be. Still, this handy tool can help you get a better idea of how much your money might grow if you assume a certain rate of return.

## How to figure out the Rule of 72

Simple words can be used to describe the Rule of 72:

Years to double = 72 x rate of return on investment (or interest rate).

The rate of interest shouldn’t be written as a number out of 1, like 0.07 for 7%. There should only be a 7. So, 72/7 is 10.3, which is the same as 10.3 years.

• To figure out simple interest, you just divide 1 by the interest rate shown as a number. If you had \$100 with a simple interest rate of 10% and no compounding, you would split 1 by 0.1 to get a rate of doubling in 10 years.
• If you want to calculate the interest that keeps adding up, you’ll get more accurate results if you use 69.3 instead of 72. The Rule of 72 is a guess, and doing mental math with 69.3 is harder than with 72, which is easy to split by 2, 3, 4, 6, 8, 9, and 12. But if you have a computer, use 69.3 to get numbers that are a little bit more exact.
• The less correct your results will be, the further away they are from an 8% gain. The Rule of 72 works best between 5 and 12 percent, but it is still only a rough estimate.
• If the interest rate is smaller, like 2%, change the 72 to 71. If the interest rate is higher, add one to the 72 for every three percentage point increase in the rate. So, if you want to figure out how long it will take for something to double at 18 percent interest, use 74.

## The Rule of 72 and how it works

The real math method is complicated and uses the time value of money to figure out how many years it will take for the amount to double. You’d start with the future value formula for periodic compounding rates of return, which helps anyone who wants to figure out how fast something is growing or shrinking:

FV = PV*(1+r)t

FV stands for “future value,” “PV” for “present value,” “r” for “rate,” and “t” for “time period.” When t is in an exponent, you can separate it by taking the natural logarithms of both sides. The natural logarithm is a way to find an exponent in math. A number’s natural logarithm is its own logarithm raised to the power of e, an irrational constant in math that is about 2.718. Using the example of doubling \$10, here’s how to figure out the Rule of

72:20 = 10*(1+r)t

20/10 = 10*(1+r)t/10

2 = (1+r)t

ln(2) = ln((1+r)t)

ln(2) = r*t

The natural log of 2 is 0.693147, so t = 0.693147/r is the answer when you use natural logarithms to solve for t.

The real results are not round numbers and are closer to 69.3, but 72 is easy to split for many of the usual rates of return that people get on their investments, so 72 has become a popular number to use to guess how long it will take to double.

Use a tool based on the full method to get more accurate information about how your investments are likely to grow.

Most families want to keep spending, often every month. If you know the average rate of return and how much you have now, you can figure out how long it will take to reach a certain goal amount. If, for example, you put \$100,000 today at 10% interest and you have 22 years until you retire, you can expect your money to double about three times, going from \$100,000 to \$200,000, then to \$400,000, and then to \$800,000.

Use the data from the Rule of 72 to help you decide how to keep saving over time if your interest rate changes or if you need more money because of inflation or other reasons.

The Rule of 72 can also help you decide between risk and profit. For example, if you have a low-risk investment that gives you 2% interest and doubles every 36 years, you can compare that to a high-risk investment that gives you 10% interest and doubles every 7 years.

When they are just starting out, many young people choose high-risk investments because they can get high rates of return for multiple doubling rounds. Those who are getting close to retirement, on the other hand, will probably choose to invest in lower-risk accounts as they get closer to their retirement goal amount since doubling is less important than investing in safer investments.

## Rule of 72 when prices go up

Investors can use the rule of 72 to figure out how long it will take for inflation to cut their buying power in half. For example, if inflation is about 8% (as it will be in the middle of 2022), you can split 72 by the inflation rate to find out how long it will be until your money is worth 50% less.

72/8 = 9 years to lose half of what you could buy.

With the Rule of 72, buyers can see for themselves how bad inflation is. Inflation might not stay high for so long, but it has in the past for several years, which really hurts the buying power of assets that have been saved up.

## Bottom Line

The Rule of 72 is a good rule of thumb to remember when deciding how much to spend. If you start investing early, even a small amount can make a big difference, and the effect can only grow as you spend more. This is because of the power of compounding. During times of inflation, you can also use the Rule of 72 to figure out how quickly your buying power can drop.