The Rule of 72 is a simple heuristic for calculating how long it will take to double your investment given a particular rate of return. Just divide 72 by the interest rate. For example, an investment earning 6% interest will take 72/6 = 12 years to double in value. The actual doubling time is LOG(2)/LOG(1 + 6%) = 11.9, but 12 is pretty close.

You can also invert the heuristic to calculate the interest rate necessary to double your investment in a particular number of years. For example, the interest rate required to double your investment in 8 years is 72/8 = 9 percent. The actual interest rate is POWER(2,1/8)-1 = 9.1%.

The Rule of 72 is most accurate for interest rates of 6% to 10%.

An alternative is the Rule of 69 , which is used for daily or continuous compounding. But part of the attraction of the Rule of 72 is the large number of small whole divisors of 72: 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36. This makes it easier to use.

Yet another alternative is the Rule of 70 , which calculates the number of years for an inflation rate to cause the value of an investment to drop in half, by dividing the inflation rate into 70. Thus it will take 70/2 = 35 years for an inflation rate of 2% to cut the value of an investment in half.

The Rule of 120 works reasonably well for calculating the time to triple an investment. 114 or 115 would be more accurate, but not nearly as divisible. The Rule of 144 works well for calculating the time to quadruple an investment. It is simply double the Rule of 72.

The derivation of these rules is rather straightforward. Pick a range of interest rates for which you want the rule to be most accurate. Say, I% = 6% through 12%. Then divide the sum of 1/LOG(1+I%) by the sum of 1/I. Multiply the result by LOG(M) where M is the multiple. In the case of M = 2, this yields 72.2. In the case of M = 3, this yields 114.5. In the case of M = 4, this yields 144.5. In the case of M = 5, this yields 167.7. In the case of M = 6, this yields 186.7. In the case of M = 7, this yields 202.8. In the case of M = 8, this yields 216.7. Then pick a nearby whole number with many divisors. For example, for M = 7 we might pick 200. Changing the range of interest rates slightly doesn't alter the result much, nor does varying a little from the calculated value. So this is a reasonably accurate method of generating such rules.

Another useful heuristic can calculate a slight underestimate of the total interest paid on an amortized loan with a level payment. Multiply the initial loan balance by the interest rate and the term of the loan, and divide the result by 2. For example, a $10,000 loan with a 4% interest rate and 10 year term would yield total payments of $10,000 * 4% * 10 / 2 = $2,000, just slightly under the actual result of $2,149. The actual result will always be higher because this is a linear approximation of the amortization curve, which is a convex curve.