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DEFINITION OF TERMS

Interest represents the difference between the principal�the value of the original capital invested�and the amount that must be repaid by the borrower after a specified term. To an investor interest is the income from invested capital. To a borrower it is the price paid for the use of money.

Interest income is usually expressed as a percentage rate of the principal per year. Thus if an invested principal of $100 earns $5.50 during a 12-month period, the rate of return is 5.5 percent. The rate of interest may be expressed in various forms, but in this chapter we will express it as either a percentage�for example, 5.5 percent�or as its equivalent decimal fraction�0.055. To obtain the interest earnings on any given principal sum for a specified period, multiply the appropriate decimal fraction by the principal sum. For example, the interest earnings on $1 invested for one year at 5.5 percent is $1 x 0.055 = $0.055, or 5� cents. The equation S = P (1 + i) represents the amount to which any given principal sum will accumulate in one year when invested at a specified rate of interest. In the equation, S represents the future value or sum at the end of the year; P represents the principal at the beginning of the year or present value; i is the rate of interest. If the principal is $1, the equation can be simplified to S = 1 + i. Once the amount to which $1 will accumulate in one year is known, the future value of any principal sum can be determined by multiplying it by that factor. Figure 14-1 shows the accumulation of interest on a principal amount of $100.

 

FIGURE 14-1
Simple Interest

The same reasoning applies to the death benefit payable under a life insurance policy. A payment deferred for one year by the beneficiary would earn interest under the policy�s interest-only option. With 5.5 percent interest the payment received on a $100,000 policy would be that original face amount plus interest at 5.5 percent for the one-year delay period. The eventual payment amount would be computed as $100,000 x 1.055 = $105,500.

The term simple interest is used if interest is paid on only the original principal invested. If interest earnings are not distributed but are added to the original principal and reinvested at the same interest rate or a different rate of interest, the result is compound interest. Compound interest is simply interest on interest. While interest may be compounded annually, semiannually, monthly, daily, or at other agreed-upon intervals, only annual compounding is illustrated in this chapter.

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