In the words of Albert Einstein, “There is no force in the universe more powerful than compound interest.”
But what can that “force” do for your investments? And how does the Rule of 72 apply?
Let’s dig into these questions and more because the answers can transform how you look at your investments.
What is the Rule of 72?
Put simply, the Rule of 72 is a formula that gives you an idea of how long it’ll take for an investment to double in value. It’s based on a fixed annual rate of return, or the amount of interest you earn on an investment in one year.
The Rule of 72 formula applies to interest rates that compound annually and is considered to work best for interest rates in the range of 6% to 10%. It’s meant to be done mentally as a quick gauge for when an investment will double in value, but you can always use a calculator to further simplify the math. We’ve included one below.
Rule of 72 formula: How do you calculate the Rule of 72?
Let’s dig into this simplified compound interest formula:
72 / Rate of Return on Investment or Interest Rate = Years to Double
Note that you should use the full number of your rate of return. For example, if you have an interest rate of 8%, you don’t want to use 0.08 in place of 8% — just use the number 8. And you can always use this calculator, if you prefer:
Rule of 72 examples
Let’s say you plan to invest $2,500 for a future vacation, and you’re wondering how long it’ll take you to double your money to $5,000. Your interest rate is currently 8%. The formula looks like this: 72/8 = 9.
In this case, it’ll take approximately nine years for your money to double to $5,000. As you can see, the Rule of 72 focuses on the interest rate, not the initial amount you have to invest.
Let’s take a look at another example. Say you currently have $500,000 saved for retirement, and you’re curious about how long it’ll take you to get to $1 million. We’ll use a 7% interest rate in this case:
72/7 = 10.3
It’ll take about 10.3 years for your money to grow to $1 million with a 7% interest rate.
One vitally important note to remember is that interest rates, particularly on investments, don’t stay the same over the course of time. Interest rates can be volatile and vary from year to year, even dipping into negative return territory. Therefore, it’s important to take that into consideration as you use the Rule of 72. It’s meant to be a quick mental gauge — not an end-all-and-be-all of calculations.
Rule of 72 chart
The Rule of 72 chart illustrates how a higher interest rate can help you double your money faster:
|Interest Rate||Rule of 72 Calculation||Years to Double Your Money|
|3%||72 / 3||24 years|
|4%||72 / 4||18 years|
|6%||72 / 6||12 years|
|8%||72 / 8||9 years|
|10%||72 / 10||7.2 years|
|12%||72 / 12||6 years|
How does compound interest impact the Rule of 72?
First, what is compound interest?
Compound interest is the interest you earn on interest. You can figure out compound interest using simple math.
Let’s say you have $100, and it earns 5% interest. At the end of year one, you’ll have $105. However, at the end of the second year, you’ll have $110.25 because you earned money on your initial $100 deposit plus $0.25 on the $5 you earned in interest after the first year. If you fast forward 30 years, you’ll have $432.19, even if you never contribute another dime to your initial $100 investment. (That’s the “powerful force” Einstein was talking about.)
The Rule of 72 is a great way to estimate how your investment will grow over time, but the formula only works for investments that compound annually. However, your investment can compound quarterly as well as semi-annually. The higher the number of compounding periods, the greater the amount of compound interest.
Related: Is There a Best Time to Invest?
The difference between the Rule of 72, the Rule of 70 and the Rule of 69.3
The Rule of 72 is focused on compounding interest that compounds annually, but if you want to determine a daily or continuous compounding interest example, you’ll get more accurate results by using 69.3 instead of 72. Here’s how it works.
Let’s say you have an investment that will give you an interest rate of 8%. Just divide it by 69.3:
69.3 / Rate of Return on Investment (Interest Rate) = Years to Double
69.3 / 8 = 8.7
In this case, the rule of 69.3 says that it would take 8.7 years for an investment to double, instead of the 9 years under the Rule of 72.
You can also use the same formula for the “Rule of 70,” like this:
70 / 8 = 8.75
Why so many different formulas? What’s the difference between 69.3 and 70?
The Rule of 70 is commonly used to compare investments with different annual interest rates. This way, you can determine how quickly you might see similar returns from each of the types of investments you’re considering … and it’s significantly easier to calculate in your head than 69.3!
How accurate is the Rule of 72?
Again, you want to keep in mind that with interest rates outside of the 6% to 10% range, the Rule of 72 doesn’t work as well.
However, you can add or subtract 1 from 72 for every 3 points the interest rate diverges from 8%. For example, the rate of 11% annual compounding interest is 3 percentage points higher than 8%, so you would add 1 to 72 to get 73 and calculate from there.
What should I learn or take away from the Rule of 72?
You may not want to use the Rule of 72 when you want a picture-perfect view of your returns (an intricate investment calculator might be a better bet). However, if you want a quick mental way to get a rough idea of how much time you’ll need to keep investing before you double your investment based on a simple interest rate, the Rule of 72 is your friend.
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