Chester is under pressure to buy a car quickly and has selected one with help from salesperson Betty. Chester can afford to buy the car in cash but Betty offers him a financing deal. With his good credit rating Chester can get an additional $2,000 off if he signs a 36-month loan with monthly payments and an interest rate of 8.0000% APR. Chester can pay the remainder of the loan off without penalty after 6 months. Assume that the car costs $40,000, so after the additional $2,000 off the amount financed for the loan is $38,000. Chesters personal discount rate is 3.5000% EAR.

a.) Compute a payment schedule for the loan: determine the monthly payment (hint: use the annuity formula) and then compute for each monthly payment: the interest component, the principal repayment, and the outstanding balance (use Excel for the computation).

b.) Compute the present value (using Chesters personal discount rate) of the cost for Chesters three options:

(i) buy the car with cash today for $40,000

(ii) take the $38,000 loan and repay after 6 months

(iii) take the $38,000 loan for the whole 36 months.

What is Chesters best option?