The Mathematics of Money

76 Chapter 2 Simple Discount

When dealing with problems with this much complexity, never try to rush through things. It is

tempting to try to just jump into plugging in and then solving with one of our formulas to get to

the answer as quickly as possible. However, as the above examples hopefully have illustrated,

the values that you need to plug into the formulas really depend entirely on whose perspective

a given question asks you to take. Take your time and think things through carefully.

Secondary Sales with Interest Rates (Optional)

When a note is sold, the maturity value is already fixed, and, as we have seen, discount is

a natural way of handling secondary sales. Nonetheless, such sales can be determined by

using simple interest instead, though the calculation will require a bit more effort.

Consider this situation, for example. A note has a maturity value of $10,000 and a

remaining term of 5 months. For what price would this note be sold if the simple interest

rate of the sale were 6%?

We cannot use the simple discount formula—this isn’t simple discount. However, we

have a problem with the simple interest formula. While we can plug in R  6% and T 

5/12, we don’t know the principal! It is tempting to plug in P  $10,000, but this would

be incorrect; $10,000 is the maturity value, not the principal, and in fact we know that

principal cannot possibly be $10,000. It must be something less, though how much less is

an open question.

We do know that maturity value is equal to principal plus interest. So:

P 
 I  $10,000

From the simple interest formula we know that I  PRT, and so we can use this in the equa-

tion above, replacing I with PRT to get:

P 
 PRT  $10,000

Substituting the known values, we get:

P 
 P(0.06)(5/12)  $10,000

P 
 P(0.025)  $10,000

The rules of algebra allow us to combine the P with the P(0.025) on the left side of this

equation through the process of combining like terms. If this is familiar to you, fine—if

not, the next step can be thought of in the following way. If you had seven P’s and put them

together with 2 P’s, it stands to reason that you would have 9 P’s altogether. In this case you

have 1 P, and when you put it together with 0.025 P’s you end up with 1.025P.

However we choose to think about it, we simplify the left side to get:

1.025(P)  $10,000

and then divide through to get:

P  $9756.10

EXERCISES 2.3

A. Basic Secondary Sales

Make sure to read the wording of each exercise carefully, especially when fi nding the remaining term of the note when it is sold.

1. Jasper Savings Bank loaned Colline $3,000 for 125 days at 8.45% simple interest then 45 days later sold the note
   to Troupsburg Trust at a simple discount rate of 7.68%. Find (a) the maturity value of the note and (b) the amount
   Tr oupsburg Trust paid for it.