The Rule of 72 (2024)

Step-by-Step Guide to Understanding the Rule of 72

Last Updated February 22, 2024

What is the Rule of 72?

The Rule of 72 is a shorthand method to estimate the number of years required for an investment to double in value (2x).

In practice, the Rule of 72 is a “back-of-the-envelope” method of estimating how long it would take an investment to double given a set of assumptions on the interest rate, i.e. rate of return.

The Rule of 72 (1)

The Rule of 72 (2)

In This Article

  • The Rule of 72 is a quick method to estimate the time needed for an investment to double in value.
  • The Rule of 72 is calculated by dividing 72 by the annualized interest rate (i.e. the rate of return).
  • Luca Pacioli, an Italian mathematician, is often credited with coming up with the Rule of 72 – albeit, there is uncertainty around its origins.
  • The Rule of 72 is a reliable approximation intended for “back-of-the-envelope” math, but the estimated number of years is still a mere approximation at the end of the day.

Table of Contents

  • How to Calculate the Rule of 72
  • The Rule of 72 Formula
  • Illustrative Rule of 72 Example
  • The Rule of 72 Chart
  • Compound Interest vs. Simple Interest: What is the Difference?
  • Rule of 72 Calculator
  • The Rule of 72 Calculation Example
  • The Rule of 115 Calculation Example

How to Calculate the Rule of 72

The Rule of 72 estimates the time needed to double the value of an investment.

The Rule of 72 is a convenient method to estimate the approximate time for invested capital to double in value.

By merely taking the number 72 and dividing it by the rate of return (or interest rate) expected to be earned, the output is the approximate number of years for an investment to double.

Therefore, the Rule of 72 is a “back of the envelope” estimate of the time to double an investment, yet the method produces a relatively accurate figure.

On that note, using Excel (or a financial calculator) is recommended for a more precise figure, especially in higher stake circ*mstances.

The Rule of 72 is well-known in finance and is perceived by most as a general rule of thumb to estimate the number of years that it would take an investment to double in value.

Yet, despite the simplicity of the calculation and convenience, the methodology is rather accurate, within a reasonable range.

The Rule of 72 Formula

The formula for the Rule of 72 divides the number 72 by the annualized rate of return (i.e. the interest rate).

Number of Years to Double = 72 ÷ Interest Rate (%)

Thus, the implied number of years for the investment’s value to double (2x) can be approximated by dividing the number 72 by the effective interest rate.

However, the effective interest rate used in the equation is not in percentage form.

Illustrative Rule of 72 Example

For example, if an investor – i.e. a limited partner (LP) of the fund — decided to contribute $200,000 to an active investor’s fund.

According to the firm’s marketing documents, the normalized return should range around 9% approximately, i.e. the 9% is the set return targeted by the fund’s portfolio of investments over the long term (and various economic cycles).

If we assume the 9% annual return is in fact achieved, the estimated number of years for the original investment to double in value is roughly 8 years.

  • Number of Years to Double (n) = 72 ÷ 9 = 8 Years

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The Rule of 72 Chart

The chart below provides the approximate number of years for an investment to double.

The left column lists the rate of return – from 1% to 10% – while the right column lists the number of years it would take for the investment to double in value based on the corresponding return.

The Rule of 72 (3)

Compound Interest vs. Simple Interest: What is the Difference?

The Rule of 72 only applies to cases of compound interest, rather than simple interest.

  • Simple Interest → The accumulated interest to date is not added back to the original principal amount.
  • Compound Interest → The interest is calculated based on the original principal, as well as the accumulated interest incurred from prior periods (“interest on interest”).

Rule of 72 Calculator

We’ll now move on to a modeling exercise, which you can access by filling out the form below.

The Rule of 72 Calculation Example

Suppose an investment earns 6.0% each year.

Q. Given the 6.0% rate of return, how many years will it take for the value of the investment to double?

If we divide 72 by 6, we can calculate the number of years it would take for the investment to double.

  • Implied Number of Years to Double (2x) = 72 ÷ 6 = 12 Years

In our illustrative scenario, the investment should double in value around 12 years.

The Rule of 115 Calculation Example

There is also a related but lesser-known rule, called the “Rule of 115”.

Number of Years to Triple = 115 ÷ Interest Rate (%)

By dividing 115 by the rate of return, the estimated time for an investment to triple (3x) can be calculated.

Continuing off the previous example with the 6% return assumption:

  • Implied Number of Years to Triple (3x) = 115 ÷ 6 = 19 Years

The Rule of 72 (7)

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calcuing

March 25, 2022 7:24 am

Rule of 72 formula offer you to have simple calculation where you can solve your equation of doubling the investment time period.

Reply

Brad Barlow

March 25, 2022 11:36 am

Reply tocalcuing

Yes, the Rule of 72 allows you to estimate the amount of time it will take to double by dividing by the rate of return.

Reply

The Rule of 72 (2024)

FAQs

What is the rule of 72 in simple terms? ›

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.

Does the rule of 72 always work? ›

It's worth noting, the “rule of 72” definition isn't necessarily perfectly accurate because past market results do not predict future market behavior. However, it's a “back of the napkin” way to determine where your portfolio might potentially be in the years ahead.

What is the rule of 72 69? ›

The Rule of 72 states that by dividing 72 by the annual interest rate, you can estimate the number of years required for an investment to double. The Rule of 69.3 is a more accurate formula for higher interest rates and is calculated by dividing 69.3 by the interest rate.

Does the rule of 72 apply to debt? ›

You can also apply the Rule of 72 to debt for a sobering look at the impact of carrying a credit card balance. Assume a credit card balance of $10,000 at an interest rate of 17%. If you don't pay down the balance, the debt will double to $20,000 in approximately 4 years and 3 months.

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.

Why does Rule 72 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.

What is the golden Rule of 72? ›

1) Rule of 72

The 'Rule of 72' gives you an estimate of the number of years it will take to double your money in a particular investment tool. You need to divide the rate of returns by 72 to know the time it would take you to double your investments.

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.

What is the magic number 72? ›

The magic number

The premise of the rule revolves around either dividing 72 by the interest rate your investment will receive, or inversely, dividing the number of years you would like to double your money in by 72 to give you the required rate of return.

What is the rule of 144? ›

The formula for the Rule of 144 is, 144 divided by the interest rate equal to the number of years it will take to quadruple your money. For instance: If you invest Rs 1,00,000 with a 12% annual expected return, then the time by which it will gain four times is 144/12 = 12 years.

What is the rule of 73? ›

Lower or higher rates outside of this range can be better predicted using an adjusted Rule of 71, 73 or 74, depending on how far they fall below or above the range. You generally add one to 72 for every three percentage point increase. So, a 15% rate of return would mean you use the Rule of 73.

What is the rule of 70? ›

The rule of 70 is used to determine the number of years it takes for a variable to double by dividing the number 70 by the variable's growth rate. The rule of 70 is generally used to determine how long it would take for an investment to double given the annual rate of return.

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 is a millionaires best friend ramsey? ›

One awesome thing that you can take advantage of is compound interest. It may sound like an intimidating term, but it really isn't once you know what it means. Here's a little secret: compound interest is a millionaire's best friend. It's really free money.

How can I double $5000 dollars? ›

To turn $5,000 into more money, explore various investment avenues like the stock market, real estate or a high-yield savings account for lower-risk growth. Investing in a small business or startup could also provide significant returns if the business is successful.

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