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.
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.
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 approach to approximate how long it will take 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.
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.
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
The Rule of 72 Chart: Implied Number of Years to Double
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.
Compound Interest vs. Simple Interest: What is the Difference?
The Rule of 72 applies to cases of compound interest, but not to 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 (i.e. “interest on interest”).
The 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
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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.
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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.
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The Rule of 72 is a nifty shortcut for approximating how long it will take an investment to double in value. It's a quick mental tool used in finance, derived by dividing 72 by the annualized interest rate, giving an estimate of the number of years required for an investment to double. This method is widely known but doesn't always provide exact figures.
This concept hinges on compound interest, where both the original principal and the accrued interest contribute to subsequent interest calculations. It's different from simple interest, where only the principal is considered in interest calculations.
The Rule of 72 formula is straightforward: Number of Years to Double = 72 ÷ Interest Rate (%). For instance, with a 9% annual return, the approximate doubling time would be 8 years (72 ÷ 9 = 8 Years).
Moreover, there's a related yet less familiar Rule of 115, which estimates the time for an investment to triple by dividing 115 by the rate of return. For instance, with a 6% return, it would take approximately 19 years to triple the investment (115 ÷ 6 = 19 Years).
Understanding these rules is crucial in finance, particularly in fields like private equity, where estimating returns and growth is fundamental. They're handy for quick estimates but might not suffice for precision in high-stakes scenarios, where using Excel or financial calculators is advisable for more accurate projections.
The distinction between compound interest and simple interest is also critical; the former involves interest on interest, while the latter only considers the principal amount.
This understanding of the Rule of 72 and its application in finance, particularly in investment analysis and projections, is essential for anyone venturing into the realm of investments, whether as an investor, financial analyst, or someone exploring private equity opportunities.
