Ch 9 Simple Interest Simple Discount Notes

Notes Notes are short term loans.  Simple Interest Notes Section 1  Simple Discount Notes This section…

$2000 Simple Interest Notes One year simple interest 6.25% for $2000. Borrower receives the face value = $2000 Interest is computed to be $125. Borrower must pay back $2125 on the maturity date of the loan. $2,000 $ $2,125

Simple Discount Notes One year simple discount 6.25% for $2000. Borrower walks out with: $1,875 Interest is computed and immediately deducted (discounted) from the face value: $125 Borrower must pay back $2,000 on the maturity date of the loan. $1,875 $ $2,000

Comparison Simple Interest Note Simple Discount Note Face Value Cost Amount Borrowed Maturity Value 1-year loan of $2,000 loan at 6.25%. $2,000 Interest:$125 I = PRT Bank Discount:$125 B = MDT $2,000 Principle $1,875 Proceeds $2,125$2,000

Using the Terminology 1 of 2 Simple discount note of $4300. Bank Discount is $285 Face Value = __________ Proceeds = __________ Bank 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. Bank discount is $750 Face Value = __________ Proceeds = __________ Bank Discount = __________ Maturity Value = __________ $12,500 $12,500 - $750$11,750 $750 $12,500

Ch 9 Simple Discount Notes Determine the bank discount and the proceeds.

Bank Discount Sample Problem 1 Bank Discount = Maturity Value x Discount Rate x Time B = MDT Maturity Value Discount Rate Time (years) B = $2000 x.06 x B = $30 Simple Discount Note $2000 6% discount rate 90 days _____ discount _____ proceeds $

Proceeds Sample Problem 1 Continued Proceeds = Maturity Value - Bank Discount P = M - B Simple Discount Note $2000 6% discount rate 90 days $30 discount P = $ $30 P = $1970 _____ proceeds$1970

Bank Discount Practice Problem Determine the bank discount: Simple Discount Note $ % discount rate 120 days $______ discount B = MDT B = $800 x.045 x B = $12 12 $______ proceeds

Sample Practice Problem Determine the proceeds: Simple Discount Note $ % discount rate 120 days $12 discount $_____ proceeds P = M - B P = $800 - $12 P = $

Compute Discount and Proceeds 1 of 1 Simple discount note with a face value of $14,250. It is an 8 month note at 8%.  Discount = _______  Proceeds = _______ B = MDT P = M - B B = 14,250 x 0.08 x = $760 P = 14,250 – 760 = $13,

Practice Ch 9, Section 3 – Simple Discount Notes Textbook Exercise 9.3 (pages 371 – 374) _____ #3 – 6, 8 – 12, 14

Compute Discount and Proceeds 2 of 2 #4, page 351 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 = P = 1,250 – = $1,192.71

Ch 9 Simple Discount Notes Computing 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 $ % discount rate 180 days $ discount $ proceeds

1 – DT Deriving the Formula for M B = P = M –P = M – MDTB MDT P = M(1 – DT) 1 – DT P = M

Computing Face Value to Achieve Desired Proceeds Proceeds received by the borrower. Discount rate used by the bank (%) Time of the loan (years) Simple Discount Note $ % discount rate 180 days $________ discount $________ proceeds $5,

Computing Face Value 1 of 2 #20, page 372 Lane Engineering needs $120,000 to install computers and network. The simple discount note has a 9.5% rate and matures in 80 days. Find the face value of the loan.

Computing Face Value 2 of 2 #26 part (a), page 373 A Malaysian 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.

Practice Ch 9, Section 3 – Simple Discount Notes Textbook Exercise 9.3 (pages 371 – 374) _____ #20, 25, 26

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 7% for 10 months. Simple discount note 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 $__________

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 7% for 10 months. Simple discount note 7% for 10 months. $3,000$2,825

Compute Effective Interest Rate Derived from: I = PRT Simple interest note 7% for 10 months. Simple discount note 7% for 10 months. $3,000 $2,825

Sample Simple Interest Note  $3000  5.8%  75 days Simple Discount Note  $3000  5.8%  75 days B = 3000 x.058 x 75/360 B = 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, Find the effective interest rate.

Objective 5 Understand U.S. Treasury Bills

U.S. Treasury Bills One way the U.S. government raises money is through the sale of U.S Treasury bills (T- bills). T-bills use discount interest. Government auctions T-bills w/ maturities of 13, 26, and 52 weeks.

Treasury Bills 1 of 1 #27, page 336 A large Japanese investment firm purchases $25,000,000 in U.S. T-bills at a 6% discount for 13 weeks. Find (a) the purchase price of the T-bills, (b) the maturity value of the T- bills, (c) the interest earned, (d) the effective rate.

Practice MathXL: Ch 8 Section 3 Homework