You simply divide 72 by the rate of appreciation and you have the approximate number of years it takes to double your money. For example at a 10% rate of appreciation it takes about 7.2 years to double your money, and at 5% it takes 72/5 = 14.4 years. At a 30% appreciation rate you double your money every 2.4 years.

At the same time you can use the formula the other way, to double your money every 5 years you need an interest rate of 14.4%.

The "proper" formula for calculating gains is (1+i)^n where i is the interest rate (as a decimal, ie 30%/100 = 0.3) and n is the number of years. A 7% interest rate over 5 years leads to a gain of (1+0.07)^5 = 1.4, ie a 40% increase. To set a profit target for your money use the rearrangement of the formula: 1+i = nth root of gain, so to quadrupal your money in 3 years means taking the cube root of four and subtracting one, ie 3root4 -1 = 0.58, you would need a gain of 58% a year compound.

Applying this to a rule of 72 problem just to check, the rule of 72 says that it takes 8 years to double your money at 9%. (1+0.09)^8 = 1.99. Pretty close, which shows that the rule of 72 is a very good quick calculator, but not an exact solution.