The term “interest” is used to indicate the rent paid for the use of money. It is also used to represent the percentage earned by an investment in a productive operation. From the lender’s point of view, the interest rate is the ratio between profit received and investment over a period of time, which is a contribution to the risk of loss, administrative costs and pure earnings or profit. From the borrower’s point of view, the interest rate can be expressed as the ratio between the amount paid for use of the funds and quantity of funds requested. In this case, the interest to be paid must be less than the earnings expected.
As money can produce earnings at a certain rate of interest by being invested for a period of time, it is important to know that one unit of money received at some future date does not produce as much earnings as a unit of money received in the present. This relationship between interest and time gives rise to the concept of the “time value of money”.
Money also has a time value, as its buying power of a dollar varies with time. During periods of inflation, the quantity of goods that can be bought with a certain amount of money decreases as the purchase date moves into the future. Although this change in the buying power of money is important, the concept of the time value of money is even more so, in that it has earning power. Any future reference to the time value of money will be restricted to this concept. Effects of inflation on the profitability of an investment are discussed in section 7.9. It is necessary to know the different methods for computing interest in order to calculate, with certainty, the actual effect of the time value of money in the comparison of alternative courses of action.
Normally, a rate of interest on a sum of money is expressed as the percentage of the sum that is paid for the use of the money during a one-year period, but it can also be quoted for different periods of time. In order to simplify the following discussion, examination of interest rates for periods other than one year will be made at the end of this Appendix (13.4). The interest to be paid on a loan, at simple interest, is proportional to the principal sum. With P as the principal sum, n the number of years and i the interest rate, simple interest can be expressed as:
I = P × n × i (B.1)
A loan at simple interest can be made for any period of time. The interest and the initial sum will be paid at the end of the loan period.
Example ;Simple Interest
Find the simple interest on US$ 4 500 at 8% per year for a) 1 year and b) 4 years.
Answer:
I = P × n × i
I = US$ 4 500 × 1 × 0.08 = US$ 360
The initial sum plus interest increases to US$ 4 860 and will be the total debt at the end of the year.
I = P ×x n × i
I = US$ 4 500 × 4 × 0.08 = US$ 1 440
When calculating the interest owed for a part of the year, it is usual to consider the year as made up of 12 months of 30 days each, that is, 360 days.
Example ;Simple Interest. Period Length Less than One Year
Find the simple interest on US$ 1000 for the period 1 February-20 April at 8 % per year.
Answer:
I = P × n × i
I = 1000 × (80 days/360 days) × 0.08
I = US$ 17.78
