How to Use the Rule of 72 to Estimate Compound Interest
The Rule of 72 is one of the most useful tools a new investor can learn because it makes it easy to estimate, quickly and efficiently, both the number of years necessary at a given rate of return to double your money and the rate of return that would be required to double a specific amount of money in a predetermined number of years. These can be fantastically convenient for back-of-the-envelope projections or planning when you don't want to whip out a set of time value of money formulas or a financial calculator.
The Rule of 72 is also useful because it demonstrates the same concept that I taught you about in an article called, You’re Spending Your Millions $1 at a Time, in which you saw just how powerful compounding can be; its ability to grow small amounts of money into large fortunes if given a period of sufficient length and a satisfactory rate of return. Internalizing this mathematical truth can cause behavioral changes to the point you prioritize your actual desires over your temporary wants, making better trade-off decisions for your own unique goals, objectives, and dreams.
How to Calculate the Rule of 72 When the Rate of Return for Your Investment Is Known
First, let's start with how to use the Rule of 72 when you have an estimated rate of return you'll earn on your investments. The formula for this derivation of the Rule of 72 is:
- Length of Time Necessary To Double Your Money = 72 divided by the investor's annual return.
An example might help you visualize the numbers. Imagine that an investor that knows he can earn 12% on his money in a given real estate investment. He may ask the question, “How long will it take to double my money at this rate of return?”.
Using our handy Rule of 72, this is a snap to calculate! All you must do is divide the magic number, 72, by the investor’s rate of return, 12. The answer, 6, is the number of years it would take to double the investment.
Furthermore, imagine that a blue chip stock investor expects to earn 8.5% on her equity holdings within a Roth IRA. She wants to know how long it will take her to double her money if this estimate turns out to be correct. To calculate this using the Rule of 72, she takes 72 and divides it by 8.5. The answer, 8.47, is the number of years it will take to turn every $1 she has invested into $2.
How to Calculate the Rule of 72 When the Number of Years Is Unknown
The Rule of 72 can also be used in reverse. An investor who wanted to double his money in a certain number of years could use the rule to discover the compound annual growth rate (CAGR) he would have to earn to achieve his goal. By comparing this with what is considered a "good" rate of return, he or she can get a better idea of whether or not expectations are reasonable.
The formula for this particular application of the Rule of 72 is:
- Required CAGR to Double Money = 72 divided by number of years in which you wish to double your money
As before, let's work through some examples so you get the hang of it.
Imagine that a local businessman in your hometown wanted to double his money in four years. To estimate a rough rate of return required to achieve such a feat, he'd use this version of the Rule of 72 and divide 72 by 4. The result, 18, represents 18%. That is the after-tax compound annual rate of return he would have to earn to meet his desired objective.
Now, imagine that a widowed retiree wants to double her wealth in twelve years. To estimate a rough rate of return required to achieve such a feat, she'd use this version of the Rule of 72 and divide 72 by 12. The result, 6, represents 6% compounded annually.
Practice Scenarios To Help You Learn How to Calculate the Rule of 72
Now that you have a basic understanding of how the Rule of 72 works, you should have no trouble answering the following questions:
Question 1: John needs to double his money in seven years to reach his financial goals. What rate of return must he earn to do this successfully?
Question 2: Susan is earning a return of 9% per annum after-taxes on her real estate holdings. How long will it take her to double her money?
Question 3: Edie currently has $5,000 in her brokerage account, but would like to double it by the time she graduates college in 3 years. Without adding any additional cash to her current balance, what rate of return must she earn in order to graduate with $10,000 in her account?
Answer 1: John would take 72 divided by 7. The answer, 10.2857%, is the amount he will need to earn on an after-tax basis to successfully reach his goal.
Answer 2: To calculate the number of years necessary to double her money using the Rule of 72, Susan would divide 72 by 9. The answer, 8, is the number of years it will take for her investment to double after taxes.
Answer 3: Edie's rate of return must be 24%. To find the answer, divide 72 by the total years Edie has to double her money, 3. Though 24% returns aren't necessarily unobtainable, it would be in Edie's best interest to continue funding her brokerage account with additional money earned along the way.