66 Chapter 2 Simple Discount
On the other hand, if we look at this note as simple interest:I PRT
$600 ($9,400)(R)(9/12)
$600 $7,050(R)
R 8.51%The 8% simple discount rate is actually equivalent to earning an 8.51% simple interest
rate. Despite initial appearances, the fund would actually earn a better return from the
8% discount note.When rates quoted for investments are based on discount, often both the interest and dis-
count rate will be given. For example, when the rates for T bills, which are discount notes,
are reported in newspapers or financial publications, it is not unusual to see both interest
and discount rates given. For example, rates for T bills might be shown in a table that
would look something like this one:U.S. TREASURY BILL CURRENT MARKET RATESMaturity Date Discount Rate Interest Rate
8/31/06 4.95% 4.97%
11/30/06 5.13% 5.20%Note that the rates differ, depending on the maturity date for the note. This will usually
be the case. The amount of time for which an investor/lender is tying up her money often
will affect the rate of interest or discount she expects to receive. The rates for longer term
notes are usually higher than for shorter term ones, though there is no reason why this must
always be the case.Rates in Disguise
Suppose that you are due a $750 paycheck at the end of the week, but want or need to get
your hands on the cash on Monday. A payday lender is an individual or business that will
offer to give you immediate cash in exchange for your agreement to sign over your check
to the lender when you receive it.^3 Suppose that such a lender offers to make this deal with
you for a fee of 2% of the paycheck. This is, for all intents and purposes, a loan. Your $750
is the maturity value, and the 2% will be calculated off of it, and subtracted from it, to
determine your proceeds.
Even though this scenario provides a classic example of discount, we need to be careful
in interpreting that 2% “rate.” It would be quite easy to think of that 2% as the simple
discount rate in the usual sense, and thus to treat it as a rate of 2% per year. But read that
description over once again—that is not the deal at all! The fee is “2% of the paycheck.” No
one said that the 2% was a rate of simple discount, annual or otherwise. The lender’s cut is
2%, not 2% “per” anything. So the lender will take a discount of (0.02)($750.00) $15.00,
leaving you with $735.00.
What is the equivalent simple discount rate? The term of the loan is 4 days, and so using
this in the formula gives:D MdT
$15.00 $750(d)(4/365)
d 1.825 182.50%A 2% fee doesn’t sound like all that much to pay, but putting it in terms of an annual simple
discount rate puts a new perspective on it. The equivalent simple interest rate is just as
astounding:I PRT
$15.00 $735(R)(4/365)
I 1.8622 186.22%(^3) This may be done by having you write a post-dated check from your own checking account.