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

Borrower receives $1875.

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

Face Value = __________

Proceeds = __________

Discount = __________

Maturity Value = __________

$4,300

$4,300 - $285$4,015

$285

$4,300

Using the Terminology 2 of 2

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

Face Value = __________

Proceeds = __________

Discount = __________

Maturity Value = __________

$12,500

$12,500 - $750$11,750

$750

$12,500

Objective 2

Find the bank discount and the proceeds.

Bank Discount

Bank Discount = Maturity Value x Discount Rate x Time

B = MDT

Maturity Value

Discount Rate

Time (years)

Simple Discount Note

$2000

6% discount rate90 days

$30 discount

$1970 proceeds

B = $2000 x .06 x 90/360

B = $30

Sample

Determine the bank discount:

Simple Discount Note

$800

4.5% discount rate

120 days

$______ discount

B = MDT

B = $800 x .045 x 120/360

B = $12

12

Proceeds

Proceeds = Maturity Value - Bank Discount

P = M - BSimple Discount Note

$2000

6% discount rate90 days

$30 discount

$1970 proceeds

P = $2000 - $30

P = $1970

Sample

Determine the proceeds:

Simple Discount Note

$800

4.5% discount rate

120 days

$12 discount

$_____ proceeds

P = M - B

P = $800 - $12

P = $788 788

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 = _______ Proceeds = _______

B = MDT

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

Discount = _______ Proceeds = _______

B = MDT

P = M - B

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 rate180 days

$166.75 discount

$5633.25 proceeds

Computing Face Value to Achieve Desired Proceeds

DT

PM

1

Proceeds received by the borrower.

Discount rate used by the bank (%)Time of the loan (years)

Simple Discount Note

$5800

5.75% discount rate180 days

$________ discount

$________ proceeds

360180

0575.1

5800M 69.971,5$M

$5,971.69

171.69

5800

Computing Face Value 1 of 2

#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.

DT

PM

1

36080

095.01

000,120

M

021111.01

000,120

9788888.0

000,120 97.587,122$

Computing Face Value 2 of 2

#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.

DT

PM

1

36045

12.01

000,720

M

015.01

000,720

985.0

000,720 47.964,730$

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

$3,000 @ 7% for 10 months.

Simple discount note

$3,000 @ 7% for 10 months.

I = PRT

I = 3000 x .07 x 10/12

I = $175

B = MDT

B = 3000 x .07 x 10/12

B = $175

Borrower gets $__________. Borrower gets $__________.3000 2825

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

$3,000 @ 7% for 10 months.

Simple discount note

$3,000 @ 7% for 10 months.

$3,000 $2,825

Compute Effective Interest Rate Derived from: I = PRT

PT

IR

Simple interest note

$3,000 @ 7% for 10 months.

Simple discount note

$3,000 @ 7% for 10 months.

$3,000

$2,825

1210

2825

175

R

0743.0R

%4.7R

Sample Simple Interest Note

$3000 5.8% 75 days

Simple Discount Note $3000 5.8% 75 days

PT

IR

36075

75.2963

25.36

R

%87.5RB = 3000 x .058 x 75/360

B = 36.25

PTR

25.36

TR

75.2963

25.36

Effective Rate of Interest

Compute Effective Interest Rate 1 of 1

#26 part (b), page 335 Japanese electric company requires proceeds of

$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.

PT

IR

36045

000,720

47.964,10

R 1218.0R %2.12R

Practice

MathXL: Ch 8 Section 3 Homework