# Discount Value

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```					Ch 8 Simple Interest

Simple Discount Notes
Objective 1

Define the basic terms used with simple
discount notes.
Simple Interest Notes

   Simple interest note for \$2000.
Borrower receives the face value = \$2000

Interest is \$125.

Borrower must pay
back \$2125 on the
maturity date of the
loan.
Simple Discount Notes

   Simple discount note for \$2000.
Face Value = \$2000

Interest is \$125.

Borrower must pay
back \$2000 on the
maturity date of the
loan.
Using the Terminology 1 of 2

   Simple discount note of \$4300.
   Interest is \$285

\$4,300
Face Value = __________
\$4,300
\$4,015 - \$285
Proceeds = __________
\$285
Discount = __________
\$4,300
Maturity Value = __________
Using the Terminology 2 of 2

   Simple discount note of \$12,500.
   Interest is \$750

\$12,500
Face Value = __________
\$12,500
\$11,750 - \$750
Proceeds = __________
\$750
Discount = __________
\$12,500
Maturity Value = __________
Objective 2

Find the bank discount and the
proceeds.
Bank Discount

   Bank Discount = Maturity Value x Discount Rate x Time

Simple Discount Note
   B = MDT
\$2000
6% discount rate
Maturity Value
90 days
Discount Rate       \$30 discount

Time (years)        \$1970 proceeds

B = \$2000 x .06 x 90/360

B = \$30
Sample

   Determine the bank discount:
Simple Discount Note
B = MDT                      \$800
4.5% discount rate

B = \$800 x .045 x 120/360      120 days
12
\$______ discount

B = \$12
Proceeds

   Proceeds = Maturity Value - Bank Discount
Simple Discount Note
   P=M-B                   \$2000
6% discount rate
90 days
P = \$2000 - \$30           \$30 discount
\$1970 proceeds
P = \$1970
Sample

   Determine the proceeds:
Simple Discount Note
P=M-B
\$800
4.5% discount rate
P = \$800 - \$12                  120 days
\$12 discount
P = \$788                          788
\$_____ proceeds
Compute Discount and Proceeds 1 of 2
   Simple discount note with a face value of
\$14,250.
   The banker discounts the 8 month note at
8%.
   Discount = _______                    B = MDT
   Proceeds = _______                    P=M-B

B = 14,250 x 0.08 x 8/12 =   \$760

P = 14,250 – 760 =   \$13,490
Compute Discount and Proceeds 2 of 2
   #4, page 333
   Face Value: \$1250
   Discount Rate: 11%
   Time: 150 days
B = MDT
   Discount = _______
P=M-B
   Proceeds = _______

B = 1,250 x 0.11 x 150/360 = 57.29

P = 1,250 – 57.29 = \$1,192.71
Objective 3

Finding the face value
Finding Face Value

   A person needs to borrow \$5800 to pay for
home improvements.
   Would a simple discount note with a face
value of \$5800 meet their needs?
Simple Discount Note

\$5800
5.75% discount rate
180 days
\$166.75 discount
\$5633.25 proceeds
Computing Face Value to Achieve Desired
Proceeds
the borrower.

P
M
1  DT
Time of the loan (years)
Discount rate used by the bank (%)

Simple Discount Note                         5800
M                            M  \$5,971.69
 180 
\$5,971.69
\$5800                                   1  .0575      
 360 
5.75% discount rate
180 days
171.69
\$________ discount
\$________ proceeds
5800
P
Computing Face Value 1 of 2               M
1  DT
   #20, page 335
   Benson automotive needs \$120,000 to
upgrade shop tools. The simple discount
note has a 9.5% rate and matures in 80 days.
    Find the face value of the loan.

120,000           120,000         120,000
M                                    \$122,587.97
1  0.095 
80      1  0.021111     0.9788888
360
P
Computing Face Value 2 of 2           M
1  DT
   #26 part (a), page 335
   Japanese electric company requires
proceeds of \$720,000 and borrows from a
bank in Thailand at 12% discount for 45 days.
    Find the face value of the loan.

720,000         720,000       720,000
M                                \$730,964.47
1  0.12 
45     1  0.015      0.985
360
Objective 4

Find the effective rate.
Comparing Interest Rates Simple Interest Notes vs
Simple Discount Notes

   Which loan “costs” more to the borrower?
Simple interest note         Simple discount note
\$3,000 @ 7% for 10 months.   \$3,000 @ 7% for 10 months.

I = PRT                      B = MDT
I = 3000 x .07 x 10/12       B = 3000 x .07 x 10/12
I = \$175                     B = \$175

3000
Borrower gets \$__________.                     2825
Borrower gets \$__________.
Effective Interest Rate

   Allows us to compare simple interest rates
with simple discount rates.

Effective Rate (APR) is the interest rate that is calculated
based on the actual amount of money received by the
borrower.

Simple interest note                    Simple discount note
\$3,000 @ 7% for 10 months.              \$3,000 @ 7% for 10 months.

\$3,000                                    \$2,825
Compute Effective Interest Rate
Simple interest note
   Derived from: I = PRT        \$3,000 @ 7% for 10 months.
\$3,000
I
R                           Simple discount note
PT                        \$3,000 @ 7% for 10 months.
\$2,825
175
R
10
2825
12

R  0.0743

R  7.4%
Sample
   Simple Interest Note                             I
   \$3000
R
PT
   5.8%
   75 days
25 .25
36
36.36.25
R
2963..75  T75
PT
2963 75 
   Simple Discount Note                                   360
   \$3000
   5.8%      B = 3000 x .058 x 75/360        R  5.87%
Effective Rate
   75 days         B = 36.25
of Interest
Compute Effective Interest Rate 1 of 1
I
   #26 part (b), page 335                       R
   Japanese electric company requires proceeds of PT
\$720,000 and borrows from a bank in Thailand at
12% discount for 45 days.
   The interest paid on the loan is \$10,964.47
    Find the effective interest rate.

10,964.47
R                     R  0.1218       R  12.2%
45
720,000 
360
Practice

   MathXL: Ch 8 Section 3 Homework

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