Simple Versus Compound Interest

Interest is payment for the use of money for a specified period of time. Interest can be calculated on either a simple or a compound basis. The distinction between the two is important because it affects the amount of interest earned or incurred.

Simple Interest

With simple interest, the interest payment is computed on only the amount of the principal for one or more periods. That is, if the original principal of the note is not changed, the interest payment will remain the same for each period. Most of the examples in this book so far have assumed simple interest. For example, if you invested $10,000 at 12% interest for three years, your yearly interest income would be $1,200 ($10,000 × 0.12).1 The total interest earned over the three years would be $3,600, and you would eventually receive $13,600 ($10,000 + $3,600).

Compound Interest

With compound interest, interest is computed on the principal of the note plus any interest that has accrued to date. That is, when compound interest is applied, the accrued interest of that period is added to the principal to determine the amount on which future interest is to be computed. Thus, by being compounded, interest is earned or incurred not only on the principal but also on the interest left on deposit.

To demonstrate the concept of compound interest, assume that the interest in the previous example now will be compounded annually rather than on a simple basis. As Table 11.1 shows, during year 1 interest income is $1,200, or 12% of $10,000. Because the interest is compounded, it is added to the principal to determine the accumulated amount of $11,200 at the end of the year. Interest in year 2 is $1,344.00, or 12% of $11,200, and the accumulated amount at the end of year 2 is now $12,544.00. The interest and the accumulated amount at the end of year 3 are calculated in the same manner. Your total interest income is $4,049.28 rather than the $3,600 you earned with simple interest.

Interest Compounded More Often Than Annually

Interest can be compounded as often as desired. The more often interest is compounded, the more quickly it will increase. For example, many financial institutions compound interest daily. This means that interest is calculated on the beginning balance of your account each day. This interest is added to the accumulated amount to determine the base for the next day’s interest calculation. Clearly, this is more advantageous than interest that is compounded yearly.

When calculating interest compounded more frequently than once a year, it is quite easy to make the necessary adjustments. For example, if interest is compounded quarterly, there are four interest periods in each year. The interest rate, which is stated in annual terms, must be reduced accordingly. Thus, instead of using an interest rate of 12% in the example, the interest rate would be 3% (12% ÷ 4 quarters) each quarter. As a general rule, the annual interest rate is divided by the number of compounding periods to determine the proper interest rate each period.

If interest is compounded quarterly in the previous $10,000, 12% example, it will equal $4,257.60, and the total amount of the investment will grow to $14,257.60. This is shown in Table 11.2. In this straightforward example, the total interest increases by $208.32, from $4,049.28 to $4,257.60 when interest is compounded quarterly instead of annually.

Exercises