The Rule of 72, 114, and 144

Rule of 72 or the “Rule of Doubling”

Most people are familiar with the Rule of 72, the simple formula that can be used to estimate how long it takes to double your money based a certain expected interest rate. For example, you expect to get an 9% rate of return on your money. At that rate, how long will it take to double your money?

To calculate this, simply divide 72 by 9 to get 8 years. For instance, if you were to invest $100 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to be worth $200; an exact calculation gives 8.0432 years.

Accuracy

The formula is reasonably accurate in the 6% to 12% range (especially in the 8% to 9% range), and progressively loses accuracy at smaller or larger values.

With 4% interest rate it will take 18.0 years to double the money
With 5% interest rate it will take 14.4 years to double the money
With 6% interest rate it will take 12.0 years to double the money
With 7% interest rate it will take 10.3 years to double the money
With 8% interest rate it will take 9.0 years to double the money
With 9% interest rate it will take 8.0 years to double the money
With 10% interest rate it will take 7.2 years to double the money

The Rule of 114 or the “Rule of Tripling”

To estimate how long it takes to triple your money, divide 114 by your expected interest rate (or rate of return). Using the 8% return figure from the first example, the formula would look like this:

114 ÷ 8 = 14.25 years

Accuracy

The higher the expected rate of return, the less accurate the formula is. However, this is also true of the Rule of 72.

Now for the Rule of 144 of the “Rule of Quadrupling”

To estimate how long it will take to quadruple your money, you can use the number 144. Simply follow the steps in the above example but substitute 144 for 114.

For more mathematical details visit wikipedia.