The Rule of 72: Definition, Usefulness, and How to Use It (2024)

What Is the Rule of 72?

The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual rate of return. Alternatively, it can compute the annual rate of compounded return from an investment, given how many years it will take to double the investment.

While calculators and spreadsheet programs like Microsoft Excel have functions to accurately calculate the precise time required to double the invested money, the Rule of 72 comes in handy for mental calculations to quickly gauge an approximate value. For this reason, the Rule of 72 is often taught to beginning investors as it is easy to comprehend and calculate. The Security and Exchange Commission also cites the Rule of 72 in grade-level financial literacy resources.

Key Takeaways

  • 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%.
  • The Rule of 72 can be applied to anything that increases exponentially, such as GDP or inflation; it can also indicate the long-term effect of annual fees on an investment's growth.
  • This estimation tool can also be used to estimate the rate of return needed for an investment to double given an investment period.
  • For different situations, it's often better to use the Rule of 69, Rule of 70, or Rule of 73.

The Rule of 72: Definition, Usefulness, and How to Use It (1)

The Formula for the Rule of 72

The Rule of 72 can be leveraged in two different ways to determine an expected doubling period or required rate of return.

Years To Double: 72 / Expected Rate of Return

To calculate the time period an investment will double, divide the integer 72 by the expected rate of return. The formula relies on a single average rate over the life of the investment. The findings hold true for fractional results, as all decimals represent an additional portion of a year.

Expected Rate of Return: 72 / Years To Double

To calculate the expected rate of interest, divide the integer 72 by the number of years required to double your investment. The number of years does not need to be a whole number; the formula can handle fractions or portions of a year. In addition, the resulting expected rate of return assumes compounding interest at that rate over the entire holding period of an investment.

The Rule of 72 applies to cases of compound interest, not simple interest. Simple interest is determined by multiplying the dailyinterest rateby the principal amount and by the number of days that elapse between payments. Compound interest is calculated on both the initial principal and the accumulated interest of previous periods of a deposit.

How to Use the Rule of 72

The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges, or loans. If thegross domestic product (GDP) grows at 4% annually, the economy will be expected to double in 72 / 4% = 18 years.

With regards to the fee that eats into investment gains, the Rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that charges 3% inannual expense feeswill reduce the investment principal to half in around 24 years. A borrower who pays 12% interest on their credit card (or any other form of loan that is charging compound interest) will double the amount they owe in six years.

The rule can also be used to find the amount of time it takes for money's value to halve due toinflation. If inflation is 6%, then a given purchasing power of the money will be worth half in around 12 years (72 / 6 = 12). If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years.

Additionally, the Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded annually. If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years.

Who Came Up With the Rule of 72?

The Rule of 72 dates back to 1494 when Luca Pacioli referenced the rule in his comprehensive mathematics book called Summa de Arithmetica. Pacioli makes no derivation or explanation of why the rule may work, so some suspect the rule pre-dates Pacioli's novel.

How Do You Calculate the Rule of 72?

Here's how the Rule of 72 works. You take the number 72 and divide it by the investment's projected annual return. The result is the number of years, approximately, it'll take for your money to double.

For example, if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money. Note that a compound annual return of 8% is plugged into this equation as 8, and not 0.08, giving a result of nine years (and not 900).

If it takes nine years to double a $1,000 investment, then the investment will grow to $2,000 in year 9, $4,000 in year 18, $8,000 in year 27, and so on.

How Accurate Is the Rule of 72?

The Rule of 72 formula provides a reasonably accurate, but approximate, timeline—reflecting the fact that it's a simplification of a more complex logarithmic equation. To get the exact doubling time, you'd need to do the entire calculation.

The precise formula for calculating the exact doubling time for an investment earning a compounded interest rate of r% per period is:

To find out exactly how long it would take to double an investment that returns 8% annually, you would use the following equation:

T = ln(2) / ln (1 + (8 / 100)) = 9.006 years

As you can see, this result is very close to the approximate value obtained by (72 / 8) = 9 years.

What Is the Difference Between the Rule of 72 and the Rule of 73?

The rule of 72 primarily works with interest rates or rates of return that fall in the range of 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from the 8% threshold. For example, the rate of 11% annual compounding interest is 3 percentage points higher than 8%.

Hence, adding 1 (for the 3 points higher than 8%) to 72 leads to using the rule of 73 for higher precision. For a 14% rate of return, it would be the rule of 74 (adding 2 for 6 percentage points higher), and for a 5% rate of return, it will mean reducing 1 (for 3 percentage points lower) to lead to the rule of 71.

For example, say you have a very attractive investment offering a 22% rate of return. The basic rule of 72 says the initial investment will double in3.27 years. However, since (22 – 8) is 14, and (14 ÷ 3) is 4.67 ≈ 5, the adjusted rule should use 72 + 5 = 77 for the numerator. This gives a value of 3.5 years, indicating that you'll have to wait an additional quarter to double your money compared to the result of 3.27 years obtained from the basic rule of 72. The period given by the logarithmic equation is3.49, so the result obtained from the adjusted rule is more accurate.

For daily orcontinuous compounding, using 69.3 in the numerator gives a more accurate result. Some people adjust this to 69 or 70 for the sake of easy calculations.

The Rule of 72: Definition, Usefulness, and How to Use It (2024)

FAQs

The Rule of 72: Definition, Usefulness, and How to Use It? ›

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.

What is the Rule of 72 and how is it used? ›

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.

In what ways can you use the Rule of 72 choose two answers? ›

Key Takeaways:
  • 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.
Aug 29, 2023

What is the equation for the Rule of 72 responses? ›

Years To Double: 72 / Expected Rate of Return

To calculate the time period an investment will double, divide the integer 72 by the expected rate of return. The formula relies on a single average rate over the life of the investment.

What is the Rule of 72 assumptions? ›

The rule of 72 is a calculation that estimates how many years it will take an investment to double in value. The calculation is based on the interest rate of the investment and the assumption that the investment's growth remains consistent.

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.”

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.

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.

Which of the following is true about the Rule of 72? ›

c.It states that the time to double your money (TDM) approximately equals 72/i, where i represents the years it takes to double your investment.

What is the Rule of 72 useful in calculating quizlet? ›

dividing 72 by the interest rate will show you how long it will take your money to double.

Is a millionaire's best friend? ›

Here's a little secret: compound interest is a millionaire's best friend.

What does "pay yourself first" mean? ›

What is a 'pay yourself first' budget? The "pay yourself first" method has you put a portion of your paycheck into your savings, retirement, emergency or other goal-based savings accounts before you do anything else with it. After a month or two, you likely won't even notice this sum is "gone" from your budget.

How to double 1000 dollars? ›

How Can I Double $1000? If your employer offers a dollar-for-dollar match contribution, you can double $1,000 by investing it in your 401(k). Other than that, there's no easy or risk-free way to double $1,000—you can invest the money in individual stocks, but there will be risks involved.

Why is the Rule of 72 useful? ›

Using the rule of 72 allows you to have a solid idea of when your investment would double just from the investment rate. Very conveniently, the number 72 divides cleanly into 1, 2, 3, 4, 6, 8, 9 and 12, allowing for a quick and simple division problem instead of your usual compound interest problem.

What is rule 72 and how does it work? ›

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.

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.

How many years does it take to double your money? ›

Very few investors know how long it takes to double their money. Rule of 72 can be of help. Divide 72 by the expected rate of return and the answer is the number of years required to double your money. For example, if a bond offers 6 percent rate of interest per year, then you will double your money in 12 years.

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

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

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