The Mathematics of Money

80

CHAPTER 2

SUMMARY

Topic Key Ideas, Formulas, and Techniques Examples

The Concept of Discount,

pp. 5 6 –5 7

• Discount is subtracted from the maturity value
  of a note


• Discount is useful when the maturity value must
  be a set amount

Discussion at beginning of

Chapter 2. 1

Calculating Simple Discount

and Proceeds, p. 5 9

• Use the simple discount formula DMdT to
  calculate discount


• Subtract discount from maturity value to fi nd
  the proceeds

A $ 5 ,000 face value discount

note has a term of 219 days.

The simple discount rate is

93 / 8 %. Find the proceeds.

(Example 2.1.2)

Finding Maturity Value,

Simple Discount Rate, and

Term, p. 60

• Plug the known quantities into the simple
  discount formula, and use the principle of
  balance to fi nd the unknown quantity


• Adjust the result using appropriate rounding
  and/or units


• Approach is the same as for similar simple
  interest problems

A $10,000 T bill with 182

days to maturity is sold at

auction for $9753.16. What

was the simple discount rate?

(Example 2.1.5)

Simple Interest Versus Simple

Discount, p. 6 4

• Regardless of how it was originally set up, a
  loan can be regarded as using simple interest or
  simple discount.


• To fi nd the simple interest rate, use the simple
  interest formula to solve for R


• To fi nd the simple discount rate, use the simple
  discount formula to solve for d

Lysander Offi ce Supply

borrowed $38,000 for 1 year.

The note’s maturity value

was $40,000. Find the simple

discount rate, and fi nd the

simple interest rate. (Example

2.2.1)

The Equivalent Simple

Interest Rate for a Discount

Note, p. 65

• Find the proceeds of the note using the simple
  discount rate and formula


• Use the proceeds as the principal in the simple
  interest formula and solve for R

A $10,000 face value,

9 -month simple discount

note is offered with an 8%

simple discount rate. What is

the equivalent simple interest

rate? (Part of Example 2.2.3)

Rates in Disguise, p. 6 6 • Discount may be expressed as a percent of the

maturity value without regard to time

• To fi nd the proceeds, multiply the percent (as
  a decimal) by the maturity value, and subtract.
  An additional fl at dollar amount may sometimes
  also be subtracted.


• An equivalent simple interest or discount rate
  can be found using the simple interest or simple
  discount formula

Ginny is expecting a $ 795

paycheck in 8 days. A

payday lender offers cash

now, charging a fee of 1.5%

plus $10. Find the equivalent

simple interest and simple

discount rates. (Example

2.2.4)

Secondary Sales of

Promissory Notes, p. 7 1

• The owner of a promissory note may sell the
  note to someone else.


• This sale does not affect the maturity value or
  maturity date of the note, so these should be
  calculated fi rst.


• The selling price is based on the previously
  determined maturity value and date.

John loans Paul $ 20 ,000 for

1 year at 8% simple interest;

3 months later, John sells

the note to Ringo at a 7¾%

simple discount rate. How

much does Ringo pay?

(Example 2.3.1)

(Continued)