The Rule of 72, Doubling Your Money, and Investment Returns (2024)

FAQs

The Rule of 72, Doubling Your Money, and Investment Returns? ›

Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.

The Rule of 72 is a calculation that estimates the number of years it takes to double your money at a specified rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. In this case, 18 years.

The Rule of 72 is a simplified formula that calculates how long it'll take for an investment to double in value, based on its rate of return. The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%.

To find the approximate number of years needed to double an investment, divide 72 by the interest rate. In this case, with an interest rate of 6.25%, divide 72 by 6.25, which is approximately 11.52. Therefore, it would take approximately 11.52 years to double the $100 investment.

However, the more precise method to calculate the exact number of years is using the exact doubling time which is 7.27 years, based on compound interest. Therefore, the correct answer to the question of how long it will take to double a $2,000 investement at 10% interest is A. 7.27 years.

Final answer:

It will take approximately 15.27 years to increase the $2,200 investment to $10,000 at an annual interest rate of 6.5%.

The table below shows the present value (PV) of $5,000 in 20 years for interest rates from 2% to 30%. As you will see, the future value of $5,000 over 20 years can range from $7,429.74 to $950,248.19.

Choice of rule

Since daily compounding is close enough to continuous compounding, for most purposes 69, 69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above, 69.3 would also be more accurate than 72. For higher annual rates, 78 is more accurate.

Errors and Adjustments

The rule of 72 is only an approximation that is accurate for a range of interest rate (from 6% to 10%). Outside that range the error will vary from 2.4% to 14.0%. It turns out that for every three percentage points away from 8% the value 72 could be adjusted by 1.

How long in years will it take a $300 investment to be worth $1000 if it is continuously compounded at 9% per year? ›

Expert-Verified Answer

It will take approximately 13.33 years for a $300 investment to grow to $1000 with continuous compounding at an annual interest rate of 9%.

The classic approach of doubling your money involves investing in a diversified portfolio of stocks and bonds and is probably the one that applies to most investors. Investing to double your money can be done safely over several years but there's more of a risk of losing most or all of your money if you're impatient.

The rule of 8-4-3 when it comes to compounding indicates a style of investment that accelerates growth with time. Initially, a corpus doubles within 8 years through an average annual return of 12% subsequently another doubling happens for the same period after another 4 years following its initial setting up.

To find out how many years it will take your investment to double, you can take 72 divided by your annual interest rate. For instance, if your savings account has an annual interest rate of 5%, you can divide 72 by 5 and assume it'll take roughly 14.4 years to double your investment.

The most basic example of the Rule of 72 is one we can do without a calculator: Given a 10% annual rate of return, how long will it take for your money to double? Take 72 and divide it by 10 and you get 7.2. This means, at a 10% fixed annual rate of return, your money doubles every 7 years.

The Rule of 72 is a simple way to determine how long an investment will take to double given a fixed annual rate of interest. Dividing 72 by the annual rate of return gives investors a rough estimate of how many years it will take for the initial investment to duplicate itself.