Doubling Your Money with the Rule of 72

In the days before computers and pocket calculators and the pre-programmed formulas and mathematical routines that come with them, people had to devise short cuts to estimate things without having to resort to lengthly pencil and paper calculations. Obviously the study of numbers and discovery of short cuts was done by people who were both good at math (which eliminates a good portion of the population) and enjoyed spending hours studying and experimenting with math (which eliminates most of the rest of us).

One of the short cuts that was developed is the Rule of 72 which states that to determine how long an investment will take to double using compound interest, simply divide 72 by the rate. Compound interest is the situation where each period's interest is added to the original investment and interest for succeeding periods is calculated on both the original investment and the interest earned in previous periods. It is this interest on interest which causes the money invested to grow so fast. Thus, if you invest $100 in an account that pays 8% compounded annually you can divide 72 by 8 to get 9 years which is when your $100 investment plus accumulated interest will have doubled to $200.

This is a short cut and, as a result, the answer will not be precise. The rule works fairly well for lower rates but becomes less accurate for rates in the higher double digit range. The method of compounding also plays a role. Simple interest is calculated and added to the account once a year. However, if the interest earned is divided by 360 (or 365) days and added to the balance for calculation purposes each day the growth will be a little faster.

The Rule of 72 explains why it is so important to begin saving early, especially in the case of retirement savings. Seeing how quickly an investment can double, depending on the rate, goes a long way to understanding how it is possible for the average individual who starts a retirement account early and contributes regularly can retire a millionaire.

The origins of this rule can be found in the book Summa de Arithmetica which was published in 1494 by Fra Luca Pacioli, an Italian monk who is also frequently referred to as the Father of Accounting or the developer/inventor of modern double entry accounting. While he is often credited with developing the double entry accounting system many historians believe that he is actually the first to describe the system, which appears to have already been in use by some business people, and popularize it with his book.