Wouldn’t it be great if you could quickly determine how much your savings could be worth in the future? Or how much you need to earn on your savings to reach a goal?
It’s easy to set a savings goal but far less easy to know if you’ll reach it. You could say “I want to have $1 million by age 65,” but how do you know if you’re saving enough to reach that goal?
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Luckily, there’s a shortcut to estimate how much your savings could be worth in the future by using something called “the rule of 72,” and the only math required is basic division.
What Is the Rule of 72?
The rule of 72 is a shortcut investors can use to estimate how long it will take their investment to double based on a fixed annual rate of return. You can also use the rule in reverse to determine roughly what rate of return you need to double your money in a given length of time.
Note that while the rule of 72 is a useful and easy rule of thumb, it doesn’t yield the most accurate results. If you need a more precise estimate, consider using an online calculator or compound growth formulas in Excel.
The Rule of 72 Formula
A key benefit of the rule of 72 is its simplicity. The formula for the rule of 72 is:
72/expected annual rate of return (R) = years to double your money (Y)
or, 72/R = Y
This means to use the rule of 72 all you do is divide 72 by the fixed rate of return to get the number of years it will take for your initial investment to double. For example, if your investment earns 6% per year on average, you would take 72 divided by 6 to determine that it will take 12 years for your money to double.
Here’s how long it would take to double your money at various rates of return, according to the rule:
| ANNUAL RATE OF RETURN (R) | YEARS TO DOUBLE (Y) |
| 1% | 72 |
| 2% | 36 |
| 3% | 24 |
| 4% | 18 |
| 5% | 14.4 |
| 6% | 12 |
| 7% | 10.3 |
| 8% | 9 |
| 9% | 8 |
| 10% | 7.2 |
Based on the above, you would need to earn 10% per year to double your money in a little over seven years.
The rule of 72 is “one of the simplest yet most powerful concepts in investment mathematics,” says Brian McGraw, a senior wealth advisor at Hightower Wealth Advisors St. Louis. It lets you “quickly assess the potential of various investment opportunities without getting bogged down in complicated formulas.”
How to Use the Rule of 72
“The rule of 72 can be used as an approximate guide to help you plan for specific financial goals that you’d like to achieve in the future,” says Amy Sabin, partner and managing director at Steward Partners.
You can apply the rule of 72 to any investment size or rate of return. While the rule is most frequently used to solve for Y — determining how many years it will take to double your money at any plugged in rate of return — it can also be used to solve for R. In other words, what rate of return do you need to earn to double your money in a set number of years?
That’s because, while the default statement of the rule is 72/R = Y, it can also be stated as 72/Y = R.
For example, if your goal is $1 million by age 65 and you are 35 currently, you know you have 30 years to reach that goal.
Based on the rule of 72, you can simply plug in the years and get your required rate of return:
72/Y = R72/30 = 2.4
So if you have $500,000 saved now, you can afford to invest it fairly conservatively for a 2.4% rate of return and still reach your $1 million goal in 30 years without making any other contributions.
“The real value of the rule will show how important it is to start saving earlier,” says Steve Azoury, a chartered financial consultant and owner of Azoury Financial. “Starting to save at age 22 versus age 29 could increase your assets twofold.”
The question is, he says: How many doubling periods will you have in your life? The answer can reveal just how aggressively you need to invest to reach your goals.
What the Rule of 72 Reveals About Investment Fees, Taxes and Inflation
The rule of 72 can also reveal the true impact of inflation and fees on your long-term investments.
“An investment that charges, say, 3% annually will reduce the returns and thus the time it takes for the investment to double,” Azoury says.
Taxes can take a similar bite out of returns, McGraw says. Economic fluctuations may also impact your investment performance over time.
Inflation has a similar effect, which you can see by using the rule of 72 in reverse, Azoury says. If a 4% positive return doubles your money in 18 years, a 4% annual inflation rate will halve your investments over the same time period. If inflation is 2% instead of 4%, it will take 36 years for your money to be reduced by half.
Who Came Up with the Rule of 72?
The rule of 72 dates back to the 15th century. It was first described in 1494 by Italian mathematician Luca Pacioli in his book “Summa de Arithmetica.” But Pacioli doesn’t explain why the rule works or how it was derived, leading some to suspect it may have been discovered even earlier. It’s sometimes erroneously attributed to Albert Einstein.
How Accurate Is the Rule of 72?
The rule of 72 is a simplified version of the future value formula, which calculates how much a sum of money will be worth in the future at a fixed rate of return.
The rule of 72 is the most accurate for rates of return between 6% and 10%. You might want to avoid using the rule of 72 for investments with low rates of return because it could suggest your money will double sooner than it actually will, says Derek Miser, investment advisor and CEO at Miser Wealth Partners.
A more accurate version of the rule of 72 would be to use 69.3 instead of 72, but you won’t get nearly as neat of numbers this way. You could also use the rule of 70, which is closer to the true time value of money, but not quite as messy as 69.3.
Another limitation of the rule of 72 is that it’s based on a constant rate of return each year, which seldom reflects reality.
“A rate of return is actually impossible to predict,” and “investments are never that consistent in real life,” Azoury says. “Unfortunately, the rule of 72 doesn’t factor in losses, and rates of return can actually change each and every year.”
The rule of 72 becomes less accurate with more volatile investment returns, which can be seen in areas like emerging-market stocks, McGraw says.
It also “doesn’t work if you’re looking for a large return in a short time frame,” Miser says. For example, if you try to apply the rule to an investment that you want to double in less than a few years, it will likely result in an unrealistic growth rate.
Alternatives to the Rule of 72
While the rule of 72 can be a helpful guide, don’t rely too heavily on its predictions because “nothing is guaranteed,” Sabin says. Even the most detailed return projections are just projections.
Spend enough time investing, and you’re bound to hear the phrase, “past returns are not indicative of future results.” So even if your investment yielded a compound annual growth rate of 6% over the past 50 years, there’s no telling what it will do next year.
As fun as all this math is, an easier way to see how much your investments will grow over time is to use a free online calculator like the savings calculator offered by U.S. News. The beauty of this calculator is it allows for future monthly contributions as well, so you can see how increasing your savings rate will impact your nest egg over the long run.
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The Rule of 72: How to Double Your Money in 7 Years originally appeared on usnews.com
