Measuring the Cost of Money

Interest is the charge added to a loan that makes up the cost of money. Interest is usually expressed as a percentage of the loan principal. The principal is the original amount of the loan. The interest rate tells you what percentage of the unpaid loan will be charged each period. The period is usually a year but may be any agreed-upon time. Here is how it works. Let's say you loan your friend $100 at 5% annual interest. At the end of a year—the period—you should receive $105, or $100 of principal and $5 interest. Simple, isn't it?

Let's say your friend doesn't repay the $100 principal, but pays you only the $5 interest; then the next year your friend will still owe you the $100 plus another $5 in interest. The preceding is an example of simple interest. Simple interest is the amount of money to be paid each period on a principal amount due.

If interest is not collected each period but allowed to accrue instead, then the accrued interest is added to the principal so that interest is charged on the preceding periods' interest as well as the unpaid principal. This is known as compound interest. Compound interest is the amount of money to be paid on the unpaid balance of a loan, including unpaid principal and interest. Most consumer credit transactions use this method of computing interest.

The time value of money is the cost of money and is measured by the interest due over the loan period.

For example, you borrow $100 at 12% annual interest compounded monthly. Although the interest is expressed as an annual rate, the period is actually a month. Each month, 1% of the unpaid balance is added to the loan, so in the first month, the unpaid balance due is $101.00; in month two, $102.01; in month three, $103.03; and so forth, until at the end of the year, the amount owed is $100 principal and $12.68 interest. While the annual percentage rate (APR) is 12%, the effective percentage rate (EPR) turns out to be 12.68%—somewhat higher. The effective percentage rate is the annual simple interest rate that would have to be charged to equal the additional interest due to compounding.

The time value of money is the cost of money and is measured by the interest due over the loan period. Here are some terms used in the computation of the time value of money. While we will not go into the formulas and computation, you should be familiar with these terms so you can use financial calculators effectively.

Present value (PV). The amount of money needed today to purchase certain goods.
Future value (FV). The amount of money at the end of the investment period equal to the present value plus accrued compound interest.
Number of periods (N). The total number of compounding periods in the term.
Rate (r). The annual interest rate divided by the number of compounding periods per year, sometimes referred to as "the discount."
Payments (PMT). Payments made to or from the investment during each compounding period, if any.
Beginning (BEG)/end (END). The time when payments are made. It can be either at the beginning of a compounding period (BEG) or at its end (END).

Using our example above, the present value is $100. Its future value is $112.68. There are 12 compounding periods (N). The rate is 1% per period (12%/12). In this example, there are no other payments at the beginning or end of a compounding period.

Here is another example using a typical mortgage loan. A $100,000 (PV) loan at 6% compounded monthly (r = 6% / 12 = 0.5%) for 30 years (N = 30 x 12 = 360 periods) has a future value of $602,258. If payments of $599.55 for principal and interest are made at the end of each month, then the total loan repayment will be only $215,838 (599.55 x 360), since some loan principal and interest were paid each compounding period. With compound interest, it pays to make principal and interest payments each month.