What Is the Rule of 72?
The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual rate of return. Alternatively, it can compute the annual rate of compounded return from an investment, given how many years it will take to double the investment.
While calculators and spreadsheet programs like Microsoft Excel have functions to accurately calculate the precise time required to double the invested money, the Rule of 72 comes in handy for mental calculations to quickly gauge an approximate value. For this reason, the Rule of 72 is often taught to beginning investors as it is easy to comprehend and calculate. The Security and Exchange Commission also cites the Rule of 72 in grade-level financial literacy resources.
Key Takeaways
- The Rule of 72 is a simplified formula that calculates how long it'll take for an investment to double in value, based on its rate of return.
- The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%.
- The Rule of 72 can be applied to anything that increases exponentially, such as GDP or inflation; it can also indicate the long-term effect of annual fees on an investment's growth.
- This estimation tool can also be used to estimate the rate of return needed for an investment to double given an investment period.
- For different situations, it's often better to use the Rule of 69, Rule of 70, or Rule of 73.
The Formula for the Rule of 72
The Rule of 72 can be leveraged in two different ways to determine an expected doubling period or required rate of return.Years To Double: 72 / Expected Rate of Return
To calculate the time period an investment will double, divide the integer 72 by the expected rate of return. The formula relies on a single average rate over the life of the investment. The findings hold true for fractional results, as all decimals represent an additional portion of a year.Expected Rate of Return: 72 / Years To Double
To calculate the expected rate of interest, divide the integer 72 by the number of years required to double your investment. The number of years does not need to be a whole number; the formula can handle fractions or portions of a year. In addition, the resulting expected rate of return assumes compounding interest at that rate over the entire holding period of an investment.
The Rule of 72 applies to cases of compound interest, not simple interest. Simple interest is determined by multiplying the daily interest rate by the principal amount and by the number of days that elapse between payments. Compound interest is calculated on both the initial principal and the accumulated interest of previous periods of a deposit.
How to Use the Rule of 72
The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges, or loans. If the gross domestic product (GDP) grows at 4% annually, the economy will be expected to double in 72 / 4% = 18 years.
With regards to the fee that eats into investment gains, the Rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that charges 3% in annual expense fees will reduce the investment principal to half in around 24 years. A borrower who pays 12% interest on their credit card (or any other form of loan that is charging compound interest) will double the amount they owe in six years.
The rule can also be used to find the amount of time it takes for money's value to halve due to inflation. If inflation is 6%, then a given purchasing power of the money will be worth half in around 12 years (72 / 6 = 12). If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years.
Additionally, the Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded annually. If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years.Who Came Up With the Rule of 72?
The Rule of 72 dates back to 1494 when Luca Pacioli referenced the rule in his comprehensive mathematics book called Summa de Arithmetica. Pacioli makes no derivation or explanation of why the rule may work, so some suspect the rule pre-dates Pacioli's novel.
How Do You Calculate the Rule of 72?
How Accurate Is the Rule of 72?
To find out exactly how long it would take to double an investment that returns 8% annually, you would use the following equation:
What Is the Difference Between the Rule of 72 and the Rule of 73?
For daily or continuous compounding, using 69.3 in the numerator gives a more accurate result. Some people adjust this to 69 or 70 for the sake of easy calculations.