The Mathematics of Money

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

Example 2.3.5 Find the simple interest rate that Chance actually earned in

Example 2.3.2.

$993.90 $1,039.52

161 days

I  PRT

$45.62  ($993.90)(R)(161/365)

$45.62  $438.405205479(R)

R  10.41%

Since Chance bought the note for less than its principal, he actually earned more than Tin-

ker would have. Moreover, since he made the purchase closer to maturity, it took him less

time to earn this larger profit. So it stands to reason that Chance’s interest rate would turn

out to be quite high compared to the original simple interest rate.

One word of caution and advice: situations such as these that involve multiple parties

are more complicated that the simpler borrower and lender problems we’ve seen in prior

sections. It is important to read carefully. Drawing time lines often helps approach these

types of problems in an organized way. An example may serve to illustrate:

Example 2.3.6 On March 1, 2005, Simon loaned Paula $12,000 at 9^3 ⁄ 8 % simple

interest. The maturity date of the note was October 17, 2005. Fifty days prior to

maturity, Simon sold the note to Randy at a simple discount rate of 8¼%. What simple

interest rate did Simon actually earn?

Original loan:

$12,000

3/1/05 9 % simple interest^38 10/17/05

October 17 is day 290 of the year; March 1 is day 60. The term of the note is thus 290 

60  230 days.

I  PRT

I  ($12,000)(0.09375)(230/365)

I  $708.90

The maturity value of the note is thus $12,000 
 $708.90  $12,708.90.

Secondary sale: We can represent the note at the time of its sale by means of a time line.

$12,708.90

10/17/05

d = 8 %^14

50 days

D  MdT

D  ($12,708.90)(0.0825)(50/365)

D  $143.63

So the selling price of the note was $12,708.90  $143.63  $12,565.27.

Simon’s P.O.V.: Since the original term was 230 days and he sold with 50 days left, Simon

was in on the deal for 180 days.

$12,000 $12,708.90

180 days

I  PRT

$565.27  ($12,000)(R)(180/365)

$565.27  5917.808219178(R)

R  9.55%.

2.3 Secondary Sales of Promissory Notes 75