The Rule Of 72: What You Need To Know To Double Your Investment

The rule of 72 can help investors figure out how long it'll take for an investment to double.

It can also determine how long it takes for a loan — or any measure affected by compound interest — to double.

How And When To Use The Rule Of 72

Say you've invested $1,000 in a stock that's expected to return 10% annually. How long will it take for your money to reach $2,000?

Divide the investment by its return: 10% of $1,000 is $1000. So, it would take 10 years for the sum to reach $2,000. Except that would be wrong because we wouldn't be taking into consideration the compounded returns of the investment.

If the stock is returning 10% a year, by the second year your investment would be worth $1,100. So, the returns of year two would be 10% of $1,100. By the third year, your investment would be worth $1,210. You can see how the calculation becomes more and more complex as time goes by.

That's why centuries ago, statisticians came up with the rule of 72. It can easily help sort out all that data into a simple, easy-to-remember formula. There are early records of the rule of 72 going back to Italian mathematicians from the 14th century.

Figure out how long an investment will take to double by dividing 72 by the expected rate of return. Put more simply, the formula would look like this:

72 / rate of return = time to double

So at 10% annual interest, $1,000 would take 7.2 years to become $2,000.

You can adapt the same formula for any time frame. For data that’s monthly-based, use that formula to understand how many months it would take for the investment to reach its double.

For instance, if an investment yields 2% a month, then it would take 36 months (72 divided by 2) to double. If you want to know how to get that rate in years, just divide the result by 12. In this case, an investment with a 2% monthly return would double in three years (36 divided by 3).

Calculating Return Rates: You can also turn the rule around if you want to know what rate of return you need for a specific sum to reach its double. Say you'd like to retire in 20 years with $1 million. What rate of return do you need if you currently have $500,000 in the bank?

You can use the following formula:

72 / number of years = rate of return needed to double.

In this case, if you divide 72 by 20 years, you get a result of 3.6% return. You can then choose to pursue low-risk investments with a relatively low return of 3.6% which will get you to your 20-year goal.

You can use the same rule in any case where there's compounded interest being added on a periodical basis, like a loan.

That means we can also use the same formula to calculate, for instance, to figure out how long it would take your credit card debt to double if you don't pay.

The rule of 72 is a simplification of a more complex mathematical equation. It gives us only approximate results. These results are the most accurate when the rate of return is 8% and still pretty accurate when the rate of return is between 6% to 10%, which are common annual returns for many types of investments like stocks, ETFs and real estate.

You can still use the rule with other rates, but it will become less and less accurate the furthest away you get from 8%. However, the rule of 72 can be adapted for any rate. To do this, simply add or subtract 1 for every 3% that the rate distances from 8%. So for a return rate of 11%, you would add 1 and use 73 instead of 72. For 14%, you would use 74% and so on. If the rate is 5%, you would subtract 1 and use 71 instead.

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