The Power of Compound Interest & the Rule of 72

Compound interest means that whenever interest is calculated, it is not being based just on the original principal (i.e., the money that you put into the account), but it based on the principal plus an prior interest that has already accumulated in the account. Because the interest is compounded, the balance will grow faster. To start with a simple example, say I invest $1 and the interest rate is 10%. The first time that interest is added, I will receive $.1 in interest (10%).

This will bring my balance of principal plus interest to $1.10. The next time interest is added, it will be calculated based on the account balance of $1.10, so I will receive $.11 in interest. Thus, the second time, I earn a little bit more interest. In this small example, it doesn't seem like much, but if you give it the power of time, compounding interest can reap huge rewards.

Here is a chart from The Motley Fool to demonstrate:

As you can see, the curves begin growing at a gradual pace but then get steeper over time. This is especially visible for the 25 year old group. The reason is that the longer the principal is invested, the more rapidly the savings build as the interest is compounded. The Motley Fool explains:

Even though each person invested the same amount of money, they have significantly different amounts at retirement. For example, Investor A began investing $5,000 a year when she was 25 years old and stopped when she was 35. For the next 30 years, she didn't contribute any more money and she didn't withdraw any money. She just left the account alone.

Investor B, on the other hand, waited until he was 35 years old and contributed $5,000 a year until he was 45. As you can see, that difference of a decade is substantial. At retirement, Investor A has $422,5671 more than Investor B - over twice as much. In fact, each investor in the chart above has more than twice as much as the person who started 10 years later (except for Investor D, of course, but she's a lot better off starting at age 55 than someone who waited until age 65).

But the above chart just depicts what would happen if each person only invested for a 10 year period. What would happen if we assume instead, that each person continued diligently saving until age 65? And how much would the 35, 45, and 55 year olds need to invest to be able to match the performance of the 25 year old?

Let's assume that each person invests in monthly installments, using the same 11% intrest rate used by The Motley Fool chart above. Using a calculator available at Bankrate.com, I estimated how much each group would accumulate by the time they reach age 65:

25 Year Olds: $3,610,408

35 Year Olds: $1,177,362

45 Year Olds: $ 363,404

55 Year Olds: $ 91,098

Next, I used the same calculator to estimate what monthly contributions the 35, 45, and 55 year olds would need to contribute in order to match the $3,610,000 accumulated by the 25 year olds:

35 Year Olds: $ 1,280 per month

45 Year Olds: $ 4,150 per month

55 Year Olds: $16,500 per month

Thus, over their respective investment periods, for each age group to accumulate approximately $3,610,000 by age 65, they would end up contributing the following amounts of principal:

25 Year Olds: $ 200,000

35 Year Olds: $ 460,800

45 Year Olds: $ 996,000

55 Year Olds: $1,980,000

As you can see, starting early can make a tremendous difference in the long run. Many 25 year olds might claim that they just don't have $416 available each month (or $5,000 annually) to invest because they have lower salaries and student loan debts to handle. This is something that I hope to post more about in the future. However, in the meantime, look at your finances long and hard-is it possible to be spending less on rent? Do you really need to upgrade your car? Do you really need to spend $8 going out to lunch each day or $1 at the vending machine. These little purchase add up. Also, don't forget the power of using your employer's 401(k) to save pre-tax dollars for retirement.

Finally, if you want a quick and dirty method for estimating how long it will take your savings to double at a given rate of compounded interest, the Rule of 72 is quite popular in the realm of personal finance. Here's how it works: Divide the expected rate of return by 72 and the result is an estimate of how many years it will take your savings to double. For example, if the expected rate of return is 9%, then the estimated time to double is 72/9, or 8 years.

The Rule of 72 is generally accurate for interest rates in the 6-10% range and it is used because it divides easily into many smaller numbers (1, 2, 3, 4, 6, 8, 9, and 12). However, if you want accurate results, you should actually use the Rule of 69.3. Thus, in the above example, the actual time to double at a 9% rate is 69.3/9 or 7.7 years. If you want to read more about the mathematics behind this rule and why it is technically the Rule of 69.3, Wikipedia has a great synopsis of the Rule of 72.