Whether or not it is worth paying $15.00 out of $750.00 to get your cash sooner is of course
a personal decision, depending entirely on your preferences and circumstances. The point
of this illustration is only that in evaluating the cost of a loan it is important to be very
clear about just what the “percent” really means. We all tend to automatically think of any
percent as an annual interest rate. That assumption can be very misleading, as this example,
hopefully, has made clear.
The fee deducted may not always be technically considered interest; some or all of it
may be considered a “service fee” or some other terminology. The technical legal treat-
ment of these fees really does not concern us here all that much though. An amount being
subtracted from the eventual payment amount is in concept discount or interest, regardless
of how it is treated for accounting or legal purposes.Example 2.2.4 Ginny is expecting a $795 paycheck in 8 days. A payday lender
offers to give her cash now for this check. The lender’s fee is 1.5% of the amount,
plus a $10 service fee. Find the equivalent simple interest and simple discount
rates.First, we need to determine how much Ginny will be giving up: 1.5% of her paycheck is
(1.5%)($795) $11.93. Adding in the $10 service fee, the total is $21.93. Ginny would
receive $795 $21.93 $773.07.As simple discount:D MdT
$21.93 ($795)d(8/365)
d 1.2586 125.86%As simple interest:I PRT
$21.93 ($773.07)R(8/365)
R 1.2943 129.43%Businesses also sometimes do something similar to raise cash. An amount that a business
is owed to be paid in the near future is called a receivable, and if a business needs cash
before the payment is due it may discount the receivable by “selling” this payment at a
discount. The amount of the discount might be expressed as a straight percent, as in our
examples above, or may be expressed as a rate. Since the difference between 2% discount
and 2% simple discount rate is so enormous, it is important to pay careful attention to how
things are worded.EXERCISES 2.2
A. TerminologyEach of the following situations could be thought of either as simple interest or as simple discount. First describe the loan in
terms of simple interest, identifying (a) the principal, (b) the maturity value, (c) the amount of interest, and (d) the face value.
Then describe the loan in terms of simple discount, identifying (e) the proceeds, (f) the maturity value, (g) the amount of
discount, and (h) the face value.- I signed a note to borrow $875 and paid back $900.
- A state government issues a bond to a group of investors. The investors pay the state $4,753,259 for the bond, and will
be paid back $5,000,000 two years later.
Copyright © 2008, The McGraw-Hill Companies, Inc.
Exercises 2.2 67cf