The Rule of 72: What It Is and How to Use It in Investing (2024)

Rate of ReturnRule of 72Actual # of YearsDifference (#) of Years

Notice that although it gives an estimate, the Rule of 72 is less precise as rates of return increase.

The Rule of 72 and Natural Logs

The Rule of 72 can estimate compounding periods using natural logarithms. In mathematics, the logarithm is the opposite concept of a power; for example, the opposite of 10³ is log base 10 of 1,000.

Ruleof72=ln(e)=1where:e=2.718281828\begin{aligned} &\text{Rule of 72} = ln(e) = 1\\ &\textbf{where:}\\ &e = 2.718281828\\ \end{aligned}Ruleof72=ln(e)=1where:e=2.718281828

e is a famous irrational number similar to pi. The mostimportantproperty of the numbereis related to the slope of exponential and logarithm functions, and its first few digits are 2.718281828.

The natural logarithm is the amount of time needed to reach a certain level of growth withcontinuous compounding.

The time value of money (TVM) formula is the following:

FutureValue=PV×(1+r)nwhere:PV=PresentValuer=InterestRaten=NumberofTimePeriods\begin{aligned} &\text{Future Value} = PV \times (1+r)^n\\ &\textbf{where:}\\ &PV = \text{Present Value}\\ &r = \text{Interest Rate}\\ &n = \text{Number of Time Periods}\\ \end{aligned}FutureValue=PV×(1+r)nwhere:PV=PresentValuer=InterestRaten=NumberofTimePeriods

To see how long it will take an investment to double, state the future value as 2 and the present value as 1.

2=1×(1+r)n2 = 1 \times (1 + r)^n2=1×(1+r)n

Simplify, and you have the following:

2=(1+r)n2 = (1 + r)^n2=(1+r)n

To remove the exponent on the right-hand side of the equation, take the natural log of each side:

ln(2)=n×ln(1+r)ln(2) = n \times ln(1 + r)ln(2)=n×ln(1+r)

This equation can be simplified again because the natural log of (1 + interest rate) equals the interest rate as the rate getscontinuously closerto zero. In other words, you are left with:

ln(2)=r×nln(2) = r \times nln(2)=r×n

The natural log of 2 is equal to 0.693 and, after dividing both sides by the interest rate, you have:

0.693/r=n0.693/r = n0.693/r=n

By multiplying the numerator and denominator on the left-hand side by 100, you can express each as a percentage. This gives:

69.3/r%=n69.3/r\% = n69.3/r%=n

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How to Adjust the Rule of 72 for Higher Accuracy

The Rule of 72 is more accurate if it is adjusted to more closely resemble the compound interest formula—which effectively transforms the Rule of 72 into the Rule of 69.3.

Many investors prefer to use the Rule of 69.3 rather than the Rule of 72. For maximum accuracy—particularly forcontinuous compounding interest rateinstruments—use the Rule of 69.3.

The number 72, however, has many convenient factors including two, three, four, six, and nine. This convenience makes it easier to use the Rule of 72 for a close approximation of compounding periods.

How toCalculate the Rule of 72 Using Matlab

The calculation of the Rule of 72 in Matlab requires running a simple command of "years = 72/return," where the variable "return" is the rate of return on investment and "years" is the result for the Rule of 72. The Rule of 72 is also used to determine how long it takes for money to halve in value for a given rate ofinflation. For example, if the rate of inflation is 4%, a command "years = 72/inflation" where the variable inflation is defined as "inflation = 4" gives 18 years. Matlab, short for matrix laboratory, is a programming platform from MathWorks used for analyzing data and more.

Does the Rule of 72 Work for Stocks?

Stocks do not have a fixed rate of return, so you cannot use the Rule of 72 to determine how long it will take to double your money. However, you still can use it to estimate what kind of average annual return you would need to double your money in a fixed amount of time. Instead of dividing 72 by the rate of return, divide by the number of years you hope it takes to double your money. For example, if you want to double your money in eight years, divide 72 by eight. This tells you that you need an average annual return of 9% to double your money in that time.

What Are 3 Things the Rule of 72 Can Determine?

There are two things the Rule of 72 can tell you reasonably accurately: how many years it will take to double your money and what kind of return you will need to double your money in a fixed period of time. Because you know how long it will take to double your money, it's also easy to figure out how long it would take to quadruple your money. For example, if you can double your money in seven years, you can quadruple it in 14 years by allowing the interest to compound.

Where Is the Rule of 72 Most Accurate?

The Rule of 72 provides only an estimate, but that estimate is most accurate for rates of return between 5% and 10%. Looking at the chart in this article, you can see that the calculations become less precise for rates of return lower or higher than that range.

The Bottom Line

The Rule of 72 is a quick and easy method for determining how long it will take to double an investment, assuming you know the annual rate of return. While it is not precise, it does provide a ballpark figure and is easy to calculate. Investments, such as stocks, do not have a fixed rate of return, but the Rule of 72 still can give you an idea of the kind of return you'd need to double your money in certain amount of time. For example, to double your money in six years, you would need a rate of return of 12%.

The Rule of 72: What It Is and How to Use It in Investing (2024)


The Rule of 72: What It Is and How to Use It in Investing? ›

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.

How does the rule of 72 apply to investing? ›

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.

How many years are needed to double a $100 investment using the rule of 72? ›

Answer and Explanation:

Applying the rule of 72, it takes about 72 / 5.75 = 12.52 years to double the investment. We can compare the approximate number to the actual number. Suppose it takes T years to double the investment at 5.75%, then we must have ( 1 + 5.75 % ) T = 2 , which yields T = 12.40.

How can you use the rule of 72 as a strategy in your own life? ›

Manage Inflation: Beyond investments, the Rule of 72 can help you understand how inflation might erode your purchasing power. By dividing 72 by the average inflation rate, you can estimate how long it'll take for the cost of living to double, aiding in long-term financial planning.

How long will it take to increase a $2200 investment to $10,000 if the interest rate is 6.5 percent? ›

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%.

Which stock will double in 3 years? ›

Stock Doubling every 3 years
S.No.NameCMP Rs.
1.Guj. Themis Bio.404.90
2.Refex Industries160.90
3.Tata Elxsi7111.75
4.Axtel Industries669.90
15 more rows

How to double $2000 dollars in 24 hours? ›

Try Flipping Things

Another way to double your $2,000 in 24 hours is by flipping items. This method involves buying items at a lower price and selling them for a profit. You can start by looking for items that are in high demand or have a high resale value. One popular option is to start a retail arbitrage business.

What is the interest rate earned on a $1400 deposit when $1800 is paid back in one year? ›

Answer and Explanation:

Therefore, the interest rate earned on the $1,400 deposit is approximately 28.57%. So, the Simple interest is $400.

What is the best Rule of 72? ›

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.

How to double 1000 dollars? ›

If your employer offers a 401(k) with matching contributions, it's entirely possible to double your $1,000 investment. How much money your company matches will vary, but many offer to match half or even all of your contributions. If they offer 100% matching, you can double your money in no time.

Does the Rule of 72 really work? ›

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%.

How to double $50,000 quickly? ›

Here's the quick rundown:
  1. Invest in real estate with Arrived.
  2. Invest in the stock market with Acorns.
  3. Invest in commercial real estate with RealtyMogul.
  4. Invest in real estate debt with Groundfloor.
Sep 27, 2023

Does a 401k double every 7 years? ›

One of those tools is known as the Rule 72. For example, let's say you have saved $50,000 and your 401(k) holdings historically has a rate of return of 8%. 72 divided by 8 equals 9 years until your investment is estimated to double to $100,000.

How long will it take $4000 to grow to $9000 if it is invested at 7% compounded monthly? ›

Substituting the given values, we have: 9000 = 4000(1 + 0.06/4)^(4t). Solving for t gives us t ≈ 6.81 years. Therefore, it will take approximately 6.76 years to grow from $4,000 to $9,000 at a 7% interest rate compounded monthly, and approximately 6.81 years at a 6% interest rate compounded quarterly.

How much is 5% interest on $50,000? ›

5% APY: With a 5% CD or high-yield savings account, your $50,000 will accumulate $2,500 in interest in one year.

How much interest will $1000 make in a year? ›

Let's look at how much you could make by depositing $1,000 into accounts with various ranges: After one year with a regular account at 0.43%: $1,004.30. After one year with a high-yield account at 4.50%: $1,045.00. After one year with a high-yield account at 5.00%: $1,050.00.

How does the rule of 72 assist savers and investors? ›

"The Rule of 72 will assist in determining how long it will take to double your money at a given rate of return," says Michael Morgan, president of TBS Retirement Planning. "For example, on an investment paying a 6% rate of return, if you divide 72 by six, it will take 12 years to double your money.

Do 90% of millionaires make over $100,000 a year? ›

Choose the right career

And one crucial detail to note: Millionaire status doesn't equal a sky-high salary. “Only 31% averaged $100,000 a year over the course of their career,” the study found, “and one-third never made six figures in any single working year of their career.”

What are the flaws of rule of 72? ›

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.

When considering saving and investing Why would you use the rule of 72? ›

The rule of 72 can help you forecast how long it will take for your investments to double. Divide 72 by the annual fixed interest rate to determine the rate at which the money would double. Historical returns on your investment type can help choose a realistic expected return rate, in some cases.


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