Richard is under pressure to find a ride quickly and signed a purchase contract for a new car with salesperson Giorgio Battistelli. Richard can afford to buy the car in cash but Giorgio offers him a financing deal. With his good credit rating and a kingdom of assets to pledge Richard can get an additional 1,000 off if he signs a 36 month loan with monthly payments and an interest rate of 8% APR. Richard can pay the loan off without penalty after 3 month. Assume that the car costs 42,000, so after the additional 1,000 off the financing volume of the loan is 41,000. Richards personal discount rate is 2% p.a EAR.

Compute a payment schedule for the loan: determine the monthly payment (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, explain the calculation for the first month on paper

Compute the present value (using Richard's discount rate) of the cost for Richard's three options: (i) buy the car in cash today for 42,000,

(ii) take the loan and repay after 3 months,

(iii) take the loan for the whole 36 months. What is Richard's best option?