Rule Of 72: What It Is And How To Use it | Bankrate (2024)

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 same calculation can also be useful for inflation, but it will reflect the number of years until the initial value has been cut in half, rather than doubling.

The Rule of 72 is derived from a more complex calculation and is an approximation, and therefore it isn’t perfectly accurate. The most accurate results from the Rule of 72 are based at the 8 percent interest rate, and the farther from 8 percent you go in either direction, the less precise the results will be.

Still, this handy formula can help you get a better grasp on how much your money may grow, assuming a specific rate of return.

The formula for the Rule of 72

The Rule of 72 can be expressed simply as:

Years to double = 72 / rate of return on investment (or interest rate)

There are a few important caveats to understand with this formula:

  • The interest rate shouldn’t be expressed as a decimal out of 1, such as 0.07 for 7 percent. It should just be the number 7. So, for example, 72/7 is 10.3, or 10.3 years.
  • The Rule of 72 is focused on compounding interest that compounds annually.
    • For simple interest, you’d simply divide 1 by the interest rate expressed as a decimal. If you had $100 with a 10 percent simple interest rate with no compounding, you’d divide 1 by 0.1, yielding a doubling rate of 10 years.
    • For continuous compounding interest, you’ll get more accurate results by using 69.3 instead of 72. The Rule of 72 is an estimate, and 69.3 is harder for mental math than 72, which divides easily by 2, 3, 4, 6, 8, 9, and 12. If you have a calculator, however, use 69.3 for slightly more accurate results.
  • The farther you diverge from an 8 percent return, the less accurate your results will be. The Rule of 72 works best in the range of 5 to 12 percent, but it’s still an approximation.
    • To calculate based on a lower interest rate, like 2 percent, drop the 72 to 71; to calculate based on a higher interest rate, add one to 72 for every three percentage point increase. So, for example, use 74 if you’re calculating doubling time for 18 percent interest.

How the Rule of 72 works

The actual mathematical formula is complex and derives the number of years until doubling based on the time value of money.

You’d start with the future value calculation for periodic compounding rates of return, a calculation that helps anyone interested in calculating exponential growth or decay:

FV = PV*(1+r)t

FV is future value, PV is present value, r is the rate and the t is the time period. To isolate t when it’s located in an exponent, you can take the natural logarithms of both sides. Natural logarithms are a mathematical way to solve for an exponent. A natural logarithm of a number is the number’s own logarithm to the power of e, an irrational mathematical constant that is approximately 2.718. With the example of a doubling of $10, deriving the Rule of 72 would look like this:

20 = 10*(1+r)t

20/10 = 10*(1+r)t/10

2 = (1+r)t

ln(2) = ln((1+r)t)

ln(2) = r*t

The natural log of 2 is 0.693147, so when you solve for t using those natural logarithms, you get t = 0.693147/r.

The actual results aren’t round numbers and are closer to 69.3, but 72 easily divides for many of the common rates of return that people get on their investments, so 72 has gained popularity as a value to estimate doubling time.

For more precise data on how your investments are likely to grow, use a compound interest calculator that’s based on the full formula.

How to use the Rule of 72 for your investment planning

Most families aim to continue investing over time, often monthly. You can project how long it takes to get to a given target amount if you have an average rate of return and a current balance.

If, for example, you have $100,000 invested today at 10 percent interest, and you are 22 years away from retirement, you can expect your money to double approximately three times, going from $100,000 to $200,000, then to $400,000, and then to $800,000.

If your interest rate changes or you need more money because of inflation or other factors, use the results from the Rule of 72 to help you decide how to keep investing over time.

You can also use the Rule of 72 to make choices about risk versus reward. If, for example, you have a low-risk investment that yields 2 percent interest, you can compare the doubling rate of 36 years to that of a high-risk investment that yields 10 percent and doubles in seven years.

Many young adults who are starting out choose high-risk investments because they have the opportunity to take advantage of high rates of return for multiple doubling cycles. Those nearing retirement, however, will likely opt to invest in lower-risk accounts as they near their target amount for retirement because doubling is less important than investing in more secure investments.

Rule of 72 during inflation

Investors can use the Rule of 72 to see how many years it will take to cut in half their purchasing power due to inflation. For example, if inflation is around 8 percent (as during the middle of 2022), you can divide 72 by the rate of inflation to get 9 years until the purchasing power of your money is reduced by 50 percent.

72/8 = 9 years to lose half your purchasing power.

The Rule of 72 allows investors to realize the severity of inflation concretely. Inflation might not remain elevated for such a long period of time, but it has done so in the past over a multi-year period, really hurting the purchasing power of accumulated assets.

Bottom Line

The Rule of 72 is an important guideline to keep in mind when considering how much to invest. Investing even a small amount can make a big impact if you start early, and the effect can only increase the more you invest, as the power of compounding works its magic. You can also use the Rule of 72 to assess how quickly you can lose purchasing power during periods of inflation.

Rule Of 72: What It Is And How To Use it | Bankrate (2024)

FAQs

Rule Of 72: What It Is And How To Use it | Bankrate? ›

How the Rule of 72 Works. For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72/10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double (1.107.3 = 2). The Rule of 72 is reasonably accurate for low rates of return.

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

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.

What is the Rule of 72 answer? ›

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.

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 rule of 70 and how does it work use an example? ›

The Rule of 70 Formula

Hence, the doubling time is simply 70 divided by the constant annual growth rate. For instance, consider a quantity that grows consistently at 5% annually. According to the Rule of 70, it will take 14 years (70/5) for the quantity to double.

Why does the 72 rule work? ›

The value 72 is a convenient choice of numerator, since it has many small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%); the approximations are less accurate at higher interest rates.

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.

What is the magic number 72? ›

“In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled,” wrote Pacioli.

Is the Rule of 72 correct? ›

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 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 to double $100,000 in a year? ›

Doubling money would require investment into individual stocks, options, cryptocurrency, or high-risk projects. Individual stock investments carry greater risk than diversification over a basket of stocks such as a sector or an index fund.

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 is the Rule of 72 useful in calculating quizlet? ›

The number of years it takes for a certain amount to double in value is equal to 72 divided by its annual rate of interest. It is only an approximation. Interest rate must remain constant.

What are some examples that the Rule of 72 could be useful for you? ›

For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72/10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double (1.107.3 = 2). The Rule of 72 is reasonably accurate for low rates of return.

What is the rule of 69 example? ›

The Rule of 69 is a simple calculation to estimate the time needed for an investment to double if you know the interest rate and if the interest is compound. For example, if a real estate investor can earn twenty percent on an investment, they divide 69 by the 20 percent return and add 0.35 to the result.

What is the best use of the rule of 70? ›

The rule of 70, also known as doubling time, calculates the years it takes for an investment to double in value. The calculation is commonly used to compare investments with different annual interest rates.

How long will it take to increase a $2200 investment to $10000 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%.

What are three things the Rule of 72 can determine? ›

dividing 72 by the interest rate will show you how long it will take your money to double. How many years it takes an invesment to double, How many years it takes debt to double, The interest rate must earn to double in a time frame, How many times debt or money will double in a period of time.

How many years will it take to double an amount at 3 percent interest? ›

If your money is in a savings account earning 3% a year, it will take 24 years to double your money (72 / 3 = 24).

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