The Mathematics of Money

60 Chapter 2 Simple Discount

Example 2.1.3 A 3-month note is discounted by $28.75. The simple discount rate is

5 ¾%. Determine the maturity value and the proceeds of the note.

D  MdT

$28.75  M(0.0575)(3/12)

$28.75  M(0.014375)

$28.75

_________0.014375  M

M  $2,000

This gives us the maturity value. To fi nd the proceeds, remember that discount is subtracted

from the maturity value. Since $2,000  $28.75  $1971.25, we conclude that the maturity

value is $2,000 and the proceeds are $1,971.25.

Example 2.1.4 When Nestor fi led his federal income taxes, he was happy to learn

that he was due a refund of $799.45. He was less happy to learn that it would take

45 days for his refund check to arrive. His tax preparer offered to give him $775.00

on the spot, in exchange for Nestor’s tax refund check when it arrives. What simple

discount rate does this offer equate to?

The amount of discount is the difference between the $799.45 and the $775.00, so D 

799.45  775.00  $24.45. Using this in the formula to fi nd the rate, we get:

D  MdT

$24.45  ($799.45)d(45/365)

$24.45  $98.56232877d

d  0.248066379

Moving the decimal place and rounding, we get that the simple discount rate is 24.81%.

Example 2.1.5 A $10,000 T bill with 182 days to maturity sold at auction for

$9,753.16. What is the simple discount rate?

The amount of discount is $10,000  $9,753.16  $246.84.

D  MdT

$246.84  ($10,000)d(182/365)

$246.84  ($4,986.3013699)d

d  0.04950363

The simple discount rate is 4.95%.

Example 2.1.6 Killawog Financial Corp invested $49,200 in discount bonds with

face values totaling $50,000. The discount rate was 4%. How long will it be until the

notes mature?

The amount of discount is $50,000  $49,200  $800.

D  MdT

$800  $50,000 (0.04)(T)

$800  $2,000 (T)

T  0.4 years

Multiplying by 365 to convert this term to days, we fi nd that the notes will mature in 146 days.

Other types of problems that we solved with simple interest can also be solved if the loan

is made using simple discount instead. The date calculation techniques of Chapter 1 can be

readily adapted to simple discount problems as well.

Example 2.1.7 The Reeds Corners Central School District borrowed $4, 959, 247

on March 7, 2005, in anticipation of receiving a state aid payment of $5, 000, 000.

The loan was based on a simple discount rate of 4 ¼%. On what date will the district

receive its state aid?

D  MdT

$40,753  $5,000,000(0.0425)(T)

T  0.1917788235 years or 70 days

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