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Even though the simple interest rate will always be higher, it does seem reasonable to
expect that, as we have seen in the examples above, the simple interest rate should be in the
same ballpark as the simple discount rate. The principal/proceeds in a given transaction (on
which the interest rate is based) are usually not far from the maturity value (on which the
discount rate is based). And so it makes sense that the rates based on them will not be too
terribly far from each other. This is not always true, though—when there is a big difference
between the principal/proceeds and maturity value, the rates can be widely different. This
will happen when the amount of interest is large in relation to the size of the loan, which
can result from very high rates and/or long terms. Some examples of these situations are
given in the Additional Exercises at the end of this section.Determining an Equivalent Simple Interest Rate
From ordinary experience, we are much more accustomed to thinking about loans from
the point of view of interest rather than discount. Thus, when we hear a discount rate,
we are likely to want to interpret it as an interest rate, even though we have just seen that
simple interest and simple discount rates are not in fact the same thing. For example, back
in Example 2.1.6 a finance company bought bonds with a 4% discount rate. You probably
thought of that as basically the same thing as earning 4% simple interest. In fact, though,
we now know that the interest rate would be a bit higher.Example 2.2.2 (Example 2.1.6 revisited) Killawog Financial invested $49,200
in bonds whose maturity values totaled $50,000. The remaining term of the bonds
was 146 days. The simple discount rate was 4%, but what would the equivalent simple
interest rate be?To answer this question, we look at the same transaction as before, but now we interpret it
as though it were simple interest. Thus:I PRT
$800 ($49,200)(R)(146/365)
$800 $19,680(R)
R 4.07%As expected, the simple interest rate is higher than the equivalent simple discount rate.Even when simple discount is the logical and natural way of looking at things, we may
want to know the equivalent simple interest rate. Since most of us are more accustomed to
thinking in terms of interest, discount rates can be deceiving. It is easy to mistakenly read
a discount rate as an interest rate. The following example will illustrate:Example 2.2.3 An investment manager is weighing a choice between two possible
investments for a fund that she manages. She originally had planned to invest in a
$10,000 face value, 9-month simple discount note issued by the Levy Pants Company,
which she was offered at a simple discount rate of 8%. On the other hand, the company
has offered to borrow the same amount of money from her fund by signing a note
carrying a simple interest rate of 8¼%. Which is the better deal for the investment fund?On the face of it, this looks like a pretty simple question; 8¼% is higher than 8%, and so
obviously a lender would prefer the higher rate.However, despite appearances, this really is not so simple, because one rate is interest, while
the other is discount, and so the comparison is not really “apples to apples.”Suppose that she invested in the 8% discount note. Then:D MdT
D ($10,000)(0.08)(9/12)
D $600And so the fund would pay $10,000 $600 $9,400 for the note.2.2 Simple Discount vs. Simple Interest 65cf
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