question archive INDIVIDUAL PROJECT Instructions • In this project, there are 2 case studies § Case 1 • Q1: 6+6 = 12 marks • Q2: 6+6 = 12 marls § Case 2 • Q1: 6 marks • Q2: 10 marks § Total of 40 marks • Answers must have correct units

Subject:MathPrice: Bought3

INDIVIDUAL PROJECT

Instructions

• In this project, there are 2 case studies § Case 1 • Q1: 6+6 = 12 marks • Q2: 6+6 = 12 marls § Case 2 • Q1: 6 marks • Q2: 10 marks § Total of 40 marks • Answers must have correct units. • Accuracy should be to the nearest cent ($1.00), percentages to the nearest 0.01%, and decimal equivalents to the nearest 0.0001for interval calculation, and 0.01 for final answer. • Each of your final answers should be in statement form with correct notation. • Final version is in PDF format

Case Study 1

Having been working for two years, Sarah has decided to purchase a car for daily commute and leisure. After hearing the advices and suggestions from friends and family, she has visited several auto dealerships, and chosen the new car she would like to purchase. She now wants to research her financing options to choose the best way to pay for the car. Sarah knows that with taxes, licence, delivery, and dealer preparation fees, the car will cost $27,650. She has $7500 from deposit account and $5000 from parents toward the purchase price but must borrow the rest. She has narrowed her financing choices to three options: dealer financing, credit union financing, and bank financing.

(i) The car dealer has offered 48-month financing at 8.5% compounded monthly.

(ii) The credit union has offered 36-month financing at 9% compounded quarterly. It has also offered 48-month financing at 9.3% compounded quarterly.

(iii) The bank has offered 36-month financing at 8.8% compounded semi-annually. It has also offered 48-month financing at 9.1% compounded semi-annually.

Sarah desires the financing option that offers the best interest rate. However, she also wants to explore the financing options that allow her to pay off her car loan more quickly. QUESTIONS 1. Sarah wants to compare the 48-month car loan options offered by the car dealer, the credit union, and the bank.

(a) What is the effective annual rate of interest for each 48-month option? - 6 marks

(b) How much interest will Sarah save by choosing the best option compared to the worst option? - 6 marks

2. Suppose Sarah wants to pay off her car loan within three years.

(a) What is the effective annual rate of interest for both of the 36-month options? - 6 marks

(b) How much interest will Sarah save by choosing the better option? - 6 marks

**Case Study 2**

Mike is planning to purchase a new pickup truck to replace the old one, and has received information (flyers, outdoor advertisings, radio, etc.) that many vehicle manufacturers are offering special deals to sell off the current year's vehicles before the new models arrive. Mike's local Ford dealership is advertising 3.9% financing for a full 48 months (i.e., 3.9% compounded monthly) or up to $8000 cash back on selected vehicles plus trade-in value (trade-in means used car is sold to the dealer for part of the payment for new car).

The vehicle that Mike wants to purchase costs $68,600 including taxes, delivery, licence, and dealer preparation. This vehicle qualifies for $5000 cash back if Mike pays cash for the vehicle, and the trade-in value for his current pickup truck is $3500. Mike has a good credit rating and knows that he could arrange an auto loan at his bank for the full price of any vehicle he chooses. His other option is to take the dealer financing offered at 3.9% for 48 months.

Mike wants to know which option requires the lower monthly payment. He knows he can use annuity formulas to calculate the monthly payment. Suppose Mike buys the vehicle on July

1)What monthly payment must Mike make if he chooses the dealer's 3.9% financing option and pays off the loan over 48 months? (Assume he makes each monthly payment at the end of the month and his first payment is due on July 31.) - 6 marks

2)When discussing details of purchasing the pickup truck, Mike is considering another model with higher price. The more expensive vehicle costs $74,900 in total and qualifies for the 3.9% dealer financing for 48 months or $2500 cash back plus trade-in value. What is the highest effective annual rate of interest at which Mike should borrow from the bank instead of using the dealer's 3.9% financing? - 10 marks