The rule of 72 is a mathematical shortcut used to determine the amount of time that it will take for an investment to double, if it is earning a fixed rate of interest. To apply the rule of 72, the number 72 is divided by the interest rate earned by the investment. The value of the answer will be the number of time periods, usually expressed in years, that will be required for the investment to double. For example, if an investment earns 12% interest annually, then it will take roughly six years to double.
As convenient a tool as the rule of 72 is, it is not exact, but rather provides an approximation. It is best suited for estimations involving investments that compound annually. For investments that compound continuously, there is a rule of 69 that is more accurate, and works the same way that the rule of 72 does. For daily compounding, the rule of 70 is often used.
The rule of 72 provides the most accurate results when the interest rate on the investment is relatively low. If the rate goes above 15 or 20%, there will be a significant inaccuracy in the answer. This is not the case, however, for the rule of 69 when calculating for continuously compounding interest, because of how the rule of 69 is mathematically derived.
It is not known how long the rule of 72 has been used for these types of estimations. References to it have been found in mathematical texts dating back to the 1400s. Even these texts do not show the derivation of the rule, suggesting that it was not a new discovery, but was probably known long before then.
A similar rule can be used to determine how long it will take for the value of a given amount of currency to halve, or in other words, to be cut in half by inflation. For this calculation, the rule of 70 is used. For example, if the average inflation rate is three percent, then we divide 70 by three to obtain 23.33. This means that the money will be worth only half as much in 23.33 years, assuming it does not earn interest.
The rule of 72 can be a valuable tool for seeing the way in which compound interest can affect your finances and therefore your life in general. An investment can double remarkably quickly if the interest rate is right, but so can a debt. This principle may have been what led to the famous saying: "Those who understand interest collect it; those who don't, pay it."