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 achieve that?
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.
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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 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.”
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 true benefit of the rule of 72 is its ability to “illustrate the time value of money and the impact a given rate of return can have on future values,” says Ronnie Gillikin, president and CEO of Capital Choice of the Carolinas.
It can shine a light on how investing too conservatively may be as detrimental as investing too aggressively.
For example, you may think you’re better off with a reliable 2% return versus a less reliable higher rate of return. But as the rule of 72 shows, this is only the case if you’re willing and able to wait 36 years for your money to double.
Even a “guaranteed” rate of return at low levels can be nothing more than “a guaranteed failure if it doesn’t meet the objectives and needs for the portfolio,” Gillikin says.
How Does the Rule of 72 Work?
The rule of 72 works for 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 equation 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 = R
72/30 = 2.4
So if you have $500,000 saved now, you can theoretically 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.
[READ: 5 of the Best Companies to Invest in for 2025 and Beyond]
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. While a handy starting point, there are many limitations to the rule of 72:
— Limited accuracy range
— Assumes a constant rate of return
— Assumes annual compounding
— Doesn’t account for taxes, inflation and fees
— Doesn’t consider contributions or withdrawals
Limited accuracy range
The rule of 72 is the most accurate for rates of return between 6% and 10%. “At very low rates below 4% or high rates above 15%, the approximation becomes less reliable,” says Nick Bour, founder and CEO of Inspire Wealth.
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.
It’s also less effective over long time periods. “The longer the time period, the more potential errors can accumulate in the rule of 72 estimation,” Bour says.
Similarly, attempting to use it on an investment you want to double in less than a few years is likely to result in an unreasonable growth rate.
Assumes a constant rate of return
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.”
Market volatility can drastically affect the actual time it takes for your money to double. “Two investments with the same average return but different volatility patterns may have very different end results,” Bour says.
The rule of 72 becomes less accurate with more volatile investment returns, which can be seen in areas like emerging-market stocks, McGraw says.
Assumes annual compounding
The rule of 72 formula assumes an annual rate of compounding. This would mean that your earnings are only reinvested once per year, which is not the case with most investments.
“Investments with more frequent compounding will double faster than the rule predicts,” Bour says.
Doesn’t account for taxes, inflation and fees
Long-term investors need to consider the impact of inflation and taxes on their future returns, Gillikin says. Inflation can erode your investment returns as fast as you accumulate them.
You can see just how big inflation’s impact is on investment returns 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.
Fees and taxes will also take a bite out of returns. “An investment that charges, say, 3% annually will reduce the returns and thus the time it takes for the investment to double,” Azoury says.
Doesn’t consider contributions or withdrawals
Lastly, the rule of 72 doesn’t account for additional contributions or withdrawals. It’s only effective for calculating the returns on a single, lump-sum investment.
If you’re adding to your investments regularly — as you hopefully are — your portfolio may grow much faster than the rule predicts. Likewise, any withdrawals you make will hinder your returns, which is why you should avoid tapping into your retirement savings early.
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 there are no guarantees in investing. 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
Update 05/21/25: This story was published at an earlier date and has been updated with new information.
