The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

Secondary sale: The remaining term is 235  74  161 days.

D  MdT

D  ($1,039.52)(0.0995)(161/365)

D  $45.62

Chance then would have paid $1,039.52  $45.62  $993.90

In this example, Tinker sold the note for less than the original principal, so he actually lost

money on the deal! This can, and does, happen. There is nothing to guarantee that a given

note can be sold for more than its original principal. If the best deal that a note’s owner can

find is to sell at a loss, so be it. If that is unacceptable, then the owner of the note has the

option of holding on until maturity, or at least until a more attractive deal comes along. It

is not the buyer’s responsibility to guarantee the seller a profit.

It is very common for a lender to sell a note prior to maturity. Government bonds (such

as the T bills discussed in the prior section, as well as other, longer term bonds) as well

as bonds of corporations are frequently bought and sold by investors and financial institu-

tions. Also, loans such as car loans and mortgages are very widely bought and sold. Since

those types of loans involve payments made during the term of the loan, though, they are

more mathematically complex and will not be dealt with in this section. But we will work

with them later in the text.

Measuring Actual Interest Rate Earned

As we discussed in Section 2.2, when simple discount is used there is often good reason to

calculate the equivalent simple interest rate as well. Similarly, when notes are bought and

sold, it is often worthwhile to calculate the actual simple interest rate earned by each party,

so that each party can evaluate the deal in terms of the interest rate earned or paid. The

following example will illustrate.

Example 2.3.3 For the scenario described in Example 2.3.1, calculate the simple

interest rate that:

(a) John actually earns

(b) Ringo actually earns (assuming he does not sell the note prior to maturity)

(c) Paul actually pays

The overall scenario has many different parts, yet in each of these cases we are asked to

look at the problem only from one party’s perspective. So to fi nd John’s interest rate, we

need to look at only what happened from John’s point of view; we can ignore everything else

that happened in the life of this note. In each case we will begin by putting ourselves in one

person’s shoes and then look at the deal only from his point of view.

Drawing time lines, while not essential, is often helpful.

(a) John made the loan at an 8% simple interest rate, and if he had held the note until

maturity that is the rate he would have earned. However, he didn’t do that, and since he sold

early the actual return on his investment may have been more or less than an 8% rate.

We can draw a time line and look at the story from John’s point of view:

$20,000 $20,344.50

3 months

From John’s viewpoint, the principal is $20,000, the interest is $344.50, and the term is

3 months.

I  PRT

$344.50  ($20,000)(R)(3/12)

$344.50  $5,000(R)

R  6.89%

So the rate John actually earned was 6.89%.

2.3 Secondary Sales of Promissory Notes 73