Sarah desires the financing option that offers the best interest rate. However,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 $8\mathrm{.}5\%$ compounded monthly.

$($ii$)$ The credit union has offered $36-$month financing at $9\%$ compounded quarterly. It has

also offered $48-$month financing at $9\mathrm{.}3\%$ compounded quarterly.

$($iii$)$ The bank has offered $36-$month financing at $8\mathrm{.}8\%$ compounded semi$-$annually. It has

also offered $48-$month financing at $9\mathrm{.}1\%$ compounded semi$-$annually. 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? $6$ marksHaving 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 $8\mathrm{.}5\%$ compounded monthly.

$($ii$)$ The credit union has offered $36-$month financing at $9\%$ compounded quarterly. It has

also offered $48-$month financing at $9\mathrm{.}3\%$ compounded quarterly.

$($iii$)$ The bank has offered $36-$month financing at $8\mathrm{.}8\%$ compounded semi$-$annually. It has

also offered $48-$month financing at $9\mathrm{.}1\%$ compounded semi$-$annually.