64 Chapter 2 Simple Discount
There is no way of knowing this for sure from the information given. We could look at
this as simple interest. In that case, we would say that:$38,000 (principal)
$2,000 (interest)
$40,000 (maturity value)But we could equally well look at this as simple discount, in which case we would say:
$40,000 (maturity value)
$2,000 (discount)
$38,000 (proceeds)In fact, we could do this for any of the loans we’ve looked at so far, whether they were
actually simple interest or simple discount. While any given loan may be set up with either
simple interest or simple discount, the reality is that interest and discount are actually just
two different ways of looking at the same thing. In many cases, interest is the more natural
way of looking at things. In others, such as the examples of Section 2.1, discount may be
more natural. In some cases there may be legal, regulatory, or accounting reasons why a
loan must be treated as interest or discount. But whichever viewpoint is more natural, the
fact remains that any simple interest loan can be looked at as discount if we want to, and
vice versa.
Without knowing any of the details surrounding this particular loan, we just can’t tell
whether it was made with interest or discount. We can, though, take a look at the deal both
ways, and use it as an example to compare simple interest and simple discount rates.Example 2.2.1 For the transaction described above fi nd (a) the simple interest rate
and (b) the simple discount rate.
(a) I PRT
$2,000 ($38,000(R)(1)
R 0.0526 5.26%(b) D MdT
$2,000 $40,000(d)(1)
d 0.05 5.00%The results of Example 2.2.1 may be surprising. You might have expected that the “rate”
would be the same either way. After all, in both cases it is a percentage, and we’ve already
seem that the amounts of simple interest and simple discount are the same (in this case, it’s
$2,000 either way.) In fact, though, the simple interest and simple discount rates are not
the same thing.
A rate is a percent, and a percent must be of something. For simple interest, that some-
thing is the principal, but in the case of simple discount, that something is the maturity
value. When we calculated the simple interest rate, we looked at $2,000 as a percent of
$38,000. With discount, the rate was found by looking at that same $2,000 as a percent
of $40,000. Since these “of ” amounts are different, it actually stands to reason that the
percents will end up being different.
In fact, we can take this observation a step further. Since the principal and maturity are
always different, for a given loan the simple interest rate and simple discount rate will
never be the same! (The only exception would be where no interest/discount is being paid.
If the interest and discount are both zero, then simple interest and simple discount rates are
both 0%.)
Notice also that in Example 2.2.1 the simple interest rate turned out to be larger than
the simple discount rate. This happened because $2,000 is a larger percentage of $38,000
than it is of $40,000. Since the principal is smaller than the maturity value, the interest rate
must be higher than the discount rate to arrive at the same $2,000. Ignoring the possible
but unlikely case of negative interest, the principal will always be less than the maturity
value for any loan. Thus, the simple interest rate will always be larger than the simple
discount rate.