The Rule of 72

If you ask an old-time banker how long it will take to double an investment at a given compound interest rate, that person will be able to give you an approximate time period in seconds. The person may use the Rule of 72. Using this rule, he or she divides the interest rate into 72. The result will be the number of years needed. As an example, suppose you want to know how long it will take to double an investment at a compound rate of 6%. The answer is about 12 years. When you divide 72 by 6, the answer is 12. The reason I'm using the word about is because the answer is an approximation. The actual mathematically accurate answer indicates that it would take a little less than 12 years for the doubling to take place. However, an approximation might be all you need.

Another example: how long will it take to double an investment at a compound rate of 18%? Dividing 72 by 18 gives a result of 4. Thus, four years is the approximate number of years it will take to double the investment. As before, the result is an approximation. The actual mathematically accurate answer indicates that it would take a little more than four years for the doubling to take place.

The answer you receive when you divide a number into 72 will not always come out even. It doesn't have to. It's OK to get a whole number and a faction as an answer. When you divide 72 by 10, as an example, the result is 7.2. This means that an amount invested at a 10% compound rate will double in a little over 7 years.

The rule of 72 is not the best rule for all percentages. For some percentages, the best rule is 70, for some, 71, etc. However, the Rule of 72 gives a good approximations for more percentages than the other numbers. Yes, the rule provides only approximations but they are very good approximations.

See if you can do these next exercises: Using the Rule of 72, calculate about how long it will require for a given investment to double in value when invested at 2%. How about for 4%, 8%, and 12%?