The Rule of 72 is a formula widely used to estimate the number of years needed to double an investment based on a specific annual rate of return. It can also be used to determine the annual rate of return required for an investment to double in a set number of years.
While calculators and spreadsheets can provide precise calculations, the Rule of 72 is a handy tool for quick mental math, making it particularly useful for rapid calculations.
The Rule of 72 can be applied in two main ways:
1. Years To Double: 72 / Expected Rate of Return
To find out how long it will take for an investment to double, divide 72 by the expected rate of return. This formula assumes a consistent average rate over the investment period, with fractional results indicating a portion of a year.
2. Expected Rate of Return: 72 / Years To Double
To find the expected return rate, divide 72 by the number of years it will take to double the investment. This works even with fractional years, assuming compounded interest at that rate throughout the investment duration.
It’s important to note that the Rule of 72 applies only to compound interest, not simple interest, which is calculated differently.
How to Apply the Rule of 72
The Rule of 72 is applicable to any scenario involving compounded growth, such as population growth, economic indicators, or loan repayments. For example, if the GDP is growing at 4% annually, it will take about 18 years to double (72 / 4 = 18).
In investment contexts, if a mutual fund charges a 3% annual fee, the investment’s value would halve in approximately 24 years. Conversely, if someone has a credit card with a 12% interest rate, their debt will double in about six years.
Additionally, the rule can help assess how inflation impacts money’s value. At a 6% inflation rate, a dollar’s purchasing power will be halved in roughly 12 years (72 / 6 = 12). If inflation drops to 4%, that timeframe extends to 18 years.
You can use this rule for various time frames as long as the return is compounded annually. For instance, if quarterly interest is 4%, it will take about 4.5 years to double the principal (72 / 4 = 18 quarters).
How to Perform the Calculation
To use the Rule of 72, simply divide 72 by the projected annual return of the investment. For instance, with an 8% annual return, it would take approximately nine years to double the investment (72 / 8 = 9). This means a $1,000 investment would grow to $2,000 in year nine, $4,000 in year eighteen, and so on.
Accuracy of the Rule of 72
While the Rule of 72 provides a useful approximation, it is not perfectly precise. To find out exactly how long it would take to double an investment that returns 8% annually, you would use the following equation:
T = ln(2) / ln (1 + (8 / 100)) = 9.006 years
As you can see, this result is very close to the approximate value obtained by (72 / 8) = 9 years.For exact calculations, you would use the formula:
Comparing the Rule of 72 and the Rule of 73
The Rule of 72 is most accurate for rates between 6% and 10%. For rates outside this range, adjustments can improve accuracy. For instance, if the rate is above 8%, you might use the Rule of 73 by adding 1 for every 3 percentage points above 8%. Conversely, you would subtract for rates below 8%.
For example, at a 22% return, using the adjusted Rule of 77 provides a doubling time of about 3.5 years, compared to the basic calculation of 3.27 years. The adjusted figure aligns closely with logarithmic calculations.
For daily or continuous compounding, using a number like 69.3 can yield a more precise result.
Conclusion
The Rule of 72 is a valuable tool for investors, offering a quick way to estimate doubling times or required rates of return. While it’s important to understand its limitations, it serves as a practical guide for making informed investment decisions.
