What Is the Rule of 72?
Let me explain the Rule of 72 to you—it's a straightforward formula that estimates how many years it will take for your invested money to double at a specific annual rate of return. You can also use it the other way around to figure out the annual compounded return rate needed if you know how many years you want it to take to double.
While you could use calculators or spreadsheets for exact figures, the Rule of 72 is perfect for quick mental math to get a rough idea. That's why I often teach it to new investors—it's simple to understand and apply. Even the SEC mentions it in their financial literacy materials for students.
Key Takeaways
Here's what you need to remember: the Rule of 72 is a basic formula that tells you how long an investment takes to double based on its return rate. It works with compounded interest and gives decent accuracy for rates from 6% to 10%. You can apply it to anything growing exponentially, like GDP or inflation, and it shows how annual fees can eat into your investment growth over time. Plus, it helps estimate the return rate required to double an investment in a set period.
Formula for the Rule of 72
You can use the Rule of 72 in two main ways to find either the doubling period or the required rate of return. To find the years to double, divide 72 by the expected rate of return. This assumes a steady average rate over the investment's life, and it works with fractions too—decimals just mean parts of a year.
To find the expected rate of return, divide 72 by the number of years you want it to take to double. Again, years don't have to be whole numbers; the formula handles fractions. The result assumes compounding at that rate throughout the holding period.
Fast Fact on Compound vs. Simple Interest
Keep in mind that the Rule of 72 is for compound interest, not simple interest. Simple interest is just the daily rate times the principal times the days between payments. Compound interest adds up on the principal plus previous interest, which is what makes the Rule of 72 work.
How to Use the Rule of 72
You can apply the Rule of 72 to anything that grows at a compounded rate, like population, economic indicators, fees, or loans. For instance, if GDP grows at 4% a year, expect the economy to double in 18 years—that's 72 divided by 4.
When it comes to fees dragging down your investments, the rule shows their long-term impact. A mutual fund with 3% annual fees will cut your principal in half in about 24 years. If you're paying 12% interest on a credit card with compound interest, your debt doubles in six years.
The rule also works for inflation: at 6%, your money's purchasing power halves in 12 years. If inflation drops to 4%, it takes 18 years instead. It handles different time frames too—as long as the rate compounds annually. For quarterly 4% interest compounded annually, it takes 18 quarters or 4.5 years to double. A 1% monthly population growth doubles in 72 months, or six years.
Who Came Up With the Rule of 72?
The Rule of 72 goes back to 1494, when Luca Pacioli mentioned it in his math book Summa de Arithmetica. He didn't explain where it came from or why it works, so some think it might be even older.
How Do You Calculate the Rule of 72?
It's simple: divide 72 by the investment's expected annual return to get the approximate years to double. For an 8% compounded annual return, that's 72 divided by 8, which is nine years. Use the whole number 8, not 0.08—otherwise, you'd get 900, which is wrong.
So, if you invest $1,000 at 8%, it grows to $2,000 in nine years, $4,000 in 18, $8,000 in 27, and so on.
What Is the Difference Between the Rule of 72 and the Rule of 73?
The Rule of 72 is best for rates between 6% and 10%. For rates outside that, adjust by adding or subtracting 1 from 72 for every 3 points away from 8%. At 11%, which is 3 points above 8%, use the Rule of 73 for better accuracy.
For daily or continuous compounding, try 69.3 instead for precision, or round to 69 or 70 for simplicity.
The Bottom Line
You can also use the Rule of 72 to see how fast debt doubles at a fixed rate. Divide 72 by the interest rate on your loan to find out how quickly it grows with minimum payments. A 20% credit card rate doubles your debt in 3.6 years.
This shows why you need to tackle high-interest debt fast to keep it from getting out of hand.
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