Understanding the Rule of 72: Explanation, Practical Value, and Implementation

What Is the Rule of 72?

The Rule of 72 is a simple and practical formula that is widely used to approximate the time it takes for an investment to double based on its annual rate of return. It can also be employed to determine the annual compound rate of return an investment will yield over a specific doubling period.

While sophisticated tools like calculators and spreadsheet programs offer precise calculations for doubling investments, the Rule of 72 is a handy mental shortcut for quick estimates. This rule is commonly taught to novice investors due to its ease of use and quick results. The Security and Exchange Commission even includes it in financial literacy resources for beginners.

Key Takeaways

• The Rule of 72 is a simplified method to determine how long it will take for an investment to double in value based on its rate of return.
• It is most accurate for interest rates between 6% and 10% and can be applied to various factors that grow exponentially, like GDP and inflation.
• It can also help estimate the rate of return needed for an investment to double within a specific time frame.
• For different scenarios, alternative rules like Rule of 69, Rule of 70, or Rule of 73 may be more suitable.

Investopedia / Daniel Fishel

The Formula for the Rule of 72

The Rule of 72 can be employed in two ways to determine either the doubling period or the required rate of return for an investment.

Years To Double: 72 / Expected Rate of Return

To find out the time for an investment to double, divide 72 by the expected rate of return. This formula assumes a consistent average rate throughout the investment period and accounts for fractions as well.

Expected Rate of Return: 72 / Years To Double

To calculate the anticipated interest rate, divide 72 by the number of years needed to double the investment. This formula handles fractional years and assumes the compounded interest rate over the investment’s entire duration.

The Rule of 72 pertains to compound interest scenarios, distinct from simple interest which calculates interest based on principal amounts only.

How to Use the Rule of 72

The Rule of 72 can be applied to anything that grows exponentially, such as population, economic indicators, charges, or loans.

For example, if a mutual fund charges 3% in annual fees, it will halve your investment in around 24 years. Likewise, a borrower paying 12% interest will double their debt in six years based on compound interest.

It can also predict how quickly money’s value decreases due to inflation. For instance, with a 6% inflation rate, money’s purchasing power will reduce by half in approximately 12 years.

The rule holds for various time frames as long as the rate of return compounds annually. For quarterly interest rates of 4%, it would take around 4.5 years to double the principal amount.

Who Came Up With the Rule of 72?

The Rule of 72 was first mentioned in 1494 by Luca Pacioli in his mathematical book Summa de Arithmetica. However, the origin of the rule may predate Pacioli’s work.

How Do You Calculate the Rule of 72?

The Rule of 72 involves dividing 72 by the projected annual return of an investment to estimate the time required for it to double.

For instance, with an 8% annual return, it would take about nine years to double an investment.

How Accurate Is the Rule of 72?

The Rule of 72 offers a reasonably accurate estimate, although it simplifies a more complex logarithmic equation for convenience.

While the exact doubling time requires a more precise calculation, the Rule of 72 provides a close approximation.

What Is the Difference Between the Rule of 72 and the Rule of 73?

The Rule of 72 is most accurate within interest rate ranges of 6% to 10%. Adjustments can be made for rates outside this range by adding or subtracting one from 72 for every three points the rate deviates from 8%.

For example, a 11% rate would use the Rule of 73 for better precision, and a 5% rate would utilize the Rule of 71.

These adjustments enhance accuracy, particularly for rates significantly differing from the typical 8% return.