## 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 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 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 circumstances.

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