Home » How does the Rule of 72 work and its understanding?

# How does the Rule of 72 work and its understanding? Photo courtesy Tyler Daviaux on Unsplash.

The rule of 72 is used to determine the time it will take for an investment to double at a given fixed rate of interest. It requires 72 to be divided by the instrument’s annual rate of interest and gives a rough estimate of the time for doubling the investment value.

The rule of 72 applies to the compounded rate of interest and is fairly accurate for interest rates that fall between 6% and 10%. It can apply to anything that grows at a compounded rate like the macroeconomic numbers, loans, bond rates, etc.

Rule of 72:

Years it takes to double your investment = 72/ Annual rate of interest.

Individuals always want to know the time it would take to double the money. They want a rough estimate of the time to double the money in order to compare different investment options. The mathematical projections for this can be quite complex so the rule of 72 provides a shortcut for the calculations and gives a simplified version of logarithmic calculation.

Let’s say the GDP of a country grows at 6% annually, the economy will double in 72/6= 12 years. As an example let’s take a bond that has a fixed coupon rate of 8%. You want to know the time it will take the investment to double and you have a goal to double the investment. The rule of 72 can be used in the same way as mentioned above and the time taken to double the money is 72/8= 9 years.

The number 72 is easily divisible so it provides a good estimation. It is best for the rate of return between 6% to 10% and most investments like index funds, mutual funds, and retirement accounts fall in this range. When dealing with interest rates outside this range the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from 8% (the middle of the rule of 72 ideal ranges). For higher interest rates the number 78 will give more accurate returns while for lower interest rates 69 or 70 would be more accurate.

Investors prefer Rule of 72 over 70 as it is convenient and has many small divisors like 1, 2, 3, 4,6,8,9, and 12. When the interest rates are lower than 6% Rule of 70 provides a good estimate.

The first reference to the rule of 72 comes from Luca Pacioli an Italian mathematician. The rule is mentioned in his 1494 book ‘Summa de Arithmetica’. The chart below gives the number of years it would take to double your money and how the rule of 72 affects your investment-