Rule of 72

The Rule of 72 is an easy to remember mathematical formula that allows investors and financial managers to quickly determine a rough estimate of how long it will take for their investment to double. In order for the Rule of 72 to be used, the investment must have a fixed annual interest rate. The formula, in which the number 72 is divided by the annual rate of return, is the reason the rule is so named.


Rule of 72 Formula


The rule of 72 calculation is simple; in order to calculate how long it will take for an investment to double, divide 72 into the annual percentage rate. For example, if the APR is 10 percent, 72 divided by 10 is 7.2. In other words, it would take approximately 7 years to double an investment at 10 percent interest. In terms of estimation, the Rule of 72 formula is fairly accurate, usually deviating less than a half a percent from the actual calculation. The Rule of 72 is most accurate with rates of return between six and ten percent, with wider deviations outside of that range. The higher the rate of return on an investment, the more the Rule of 72 deviates, so for very high rates it may be best to actually calculate how soon the investment will double.

The Rule of 72 is actually based on an ancient mathematical formula that has been in existence since the 15th Century and probably earlier. The first written reference to the Rule of 72 is in the Summa de Arithmetica by Luca Pacioli of Venice, but even his writing about the rule seems to assume an already established existence.

Building on the Rule of 72


For those interested in a more accurate formula than the Rule of 72, a secondary rule called the Eckart-McHale rule, or E-M rule, offers a multiplier that can help offset the Rule of 72 deviation. The E-M rule suggests using 69.3 or 70 instead of 72 for the initial division, then provides a complex formula for making the estimate more accurate by using a multiplier based on the interest rate to account for any deviation. However, if you are simply looking for a quick and easy estimate of an investment’s time to double, the Rule of 72 is the accepted guideline.

Applications of the Rule of 72


One thing to keep in mind is that the Rule of 72 is only useful with compound interest situations, such as investments, and not simple interest options, such as savings accounts. Also, the Rule of 72 should never be used for making serious investment decisions without first calculating the real investment required to meet investor needs.

The Rule of 72, and the number 72, was chosen because of its relative ease in dividing into most numbers, making it easy mental math. However, outside of the six to ten percent interest rate range, other numbers may be more accurate. As well, it is important to keep in mind that the formula only tells you how many periods it will take to double your money, and it is often assumed that you will use an annual percentage rate, if you use a monthly or quarterly rate, you need to realize that the number you calculate will refer to the number of periods specified by the rate used.
Tim Ord
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