Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 1 Chapter 9 Simple Interest Section 3 Simple Discount Notes

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 2 Simple Interest versus Simple Discount Notes Simple Interest Face Value + Interest = Maturity Value (Principal) Simple Discount Proceeds + Discount = Face Value (Interest) (Maturity Value)

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3 Calculating Bank Discount Bank discount = Face value × Discount Rate × Time or B = MDT where B = Bank Discount D = Discount Rate M = Face value (maturity) T = Time (in yrs)

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 4 Calculating Bank Discount Then, if P is the proceeds, Proceeds (loan amount) = Face value – Bank discount or P = M – B Stated another way, Face value = Proceeds (loan amount) + Bank discounts or M = P + B

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 5 Example Jessica Samson signs a simple discount note with a face or maturity value of $22,000 so that she can purchase a car. The banker discounts the 10-month note at 5%. Find the amount of the discount and the proceeds.

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 6 Example (cont) Samson does not receive $22,000 from the bank— that is the amount she must repay when the loan matures. Use M = $22,000, D = 5%, and T = 10/12 in the formula B = MDT to find the discount, which is the interest that must be paid at maturity. Bank Discount = M × D × T B = $22,000 ×.05 × 10/12 = $916.67

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 7 Example (cont) The discount of $ is the interest. Proceeds are found using P = M – B P = $22,000 – $ = $ Samson signs the discount note with a face value of $22,000, but receives $21, Ten months later she must pay $22,000 to the bank.

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 8 Calculating Face Value to Achieve Desired Proceeds where M = Face value of the simple discount note P = Proceeds received by the borrower D = Discount rate used by the bank T = Time of the loan (in years)

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 9 Example Sam Swanson purchased a classic 1970 Mustang and plans to rebuild it. He estimates that he will need to borrow $15,000 for 270 days. Find the face value of the 9% simple discount note that would result in proceeds of $15,000 to Swanson.

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 10 Example Jeff Wellner of Wellner Automotive has been offered loans from two different banks. Each note has a face value of $80,000 and a time of 180 days. One note has a simple interest rate of 10%, and the other a simple discount rate of 10%. Wellner wants to know which is the better deal.

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 11 Find the Effective Interest Rate Truth in Lending Act – 1969 Effective Rate of Interest – also called Annual Percentage Rate, APR, True Rate Interest rate is calculated based on the actual amount received by the borrower. Stated Rate, or Nominal Rate – is the rate written on the note (it is NOT the effective rate)

Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 12 Example Find the effective rate of interest (APR) for the simple discount note of the previous example. Recall that I = $4000 (the discount), P = $86,000 (the proceeds), and T = 180/360.