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.
How to Calculate Rule of 72?
The Rule of 72 is a convenient approach to approximate how long it will take for invested capital to double in value.
In order to figure out the number of years it would take to double an investment, 72 is divided by the investmentās annual return.
The calculation is more so a rough estimate ā i.e. āback of the envelopeā math ā that provides a relatively accurate figure.
For a more precise figure, using Excel (or a financial calculator) is recommended.
The Rule of 72 is well-known in finance and 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, in spite of the simplicity of the calculation and the convenience, the methodology is rather accurate, within a reasonable range.
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).
Thus, the implied number of years for the investmentās 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.
For example, if an investor decided to contribute $200,000 to an active investorās 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 fundās 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 Ć· 9 = 8 Years
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 ā from 1% to 10% ā while the right column states the number of years it would take for the investment to double in value based on the corresponding return.
The Rule of 72: Compound Interest vs. Simple Interest
The Rule of 72 applies to cases of compound interest, but not to simple interest.
- Simple Interest ā The accumulated interest to date is NOT added back to the original principal amount.
- Compound Interest ā The interest is calculated based on the original principal, as well as the accumulated interest incurred from prior periods (i.e. āinterest on interestā).
Rule of 72 Calculator
Weāll now move to a modeling exercise, which you can access by filling out the form below.
1. Rule of 72 Calculation Example
Letās say, for example, an investment is earning 6% each year.
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 Ć· 6 = 12 Years
In our illustrative scenario, the investment needs around 12 years before doubling in value.
2. Rule of 115 Calculation Example
There is also a related but lesser-known rule, called the āRule of 115ā.
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 Ć· 6 = 19 Years
