In finance, the rule of 72 and the rule of 70 are methods for estimating the doubling time of an investment. The number referred to in the rule is divided by the interest rate over the period (usually years) to obtain an approximation of the number of periods required for doubling. Although modern scientific calculators and spreadsheets have functions to find the doubling time with greater accuracy, these rules are still useful when one has to do a quick mental calculation or when one has a simple calculator at hand.
These rules apply under the assumptions of exponential growth and are then used for calculations related to anatocism (or compound interest), as opposed to simple interest, or exponential decreasing, and are in that case used to calculate the half-life. The choice of which number to use depends on the various occasions: 69 is more accurate in the case of continuous compound interest, while 72 works better with more common interest situations and is more easily divisible. There are then several variations of these rules designed to increase their accuracy.
Example of the use of rules 70 and 72
To get an estimate of the periods required to double the original capital invested, one must divide the "rule quantity" by the expected growth rate, expressed as a percentage.
For example, considering an initial investment of €100 with a compound interest rate of 9 percent per year, according to the rule of 72 it takes 72/9 = 8 years for the invested amount to reach €200. In comparison, an exact calculation returns the result: ln(2)/ln(1+0.09) = 8.0432 years.
Similarly, to determine the time required for the halving of a certain amount given a given rate, one divides the "rule number" by the rate.
To determine the time it takes for the purchasing power of money to halve, simply divide the "rule number" by the inflation rate. Thus, considering an inflation rate of 3.5 percent and using the "rule of 70," we get a period of 70/3.5 = 20 years for purchasing power to halve.
To estimate the impact of additional fees on financial policies, i.e., insurance investment instruments with high flexibility and financial content, (e.g., mutual fund shares and fees, loads or foreign exchange charges on investment portfolios of variable universal life insurance, etc...), we divide 72 by the fee.