Question

Christie is buying a new car today and is paying a $7500 cash down payment. She will finance the balance at 7.25 percent interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. Which one of the following statements is correct concerning this purchase?

A. The future value of the loan is equal to 37 x 450.

B. The present value of the car is equal to $7500 + (36 × $450).

C. The $7500 is the present value of the purchase.

D. To compute the initial loan amount, you must use a monthly interest rate.

E. The car loan is an annuity due.

Answer 1

D. To compute the initial loan amount, you must use a monthly interest rate.

The question is based on present value analysis.A car is purchased against which some cash has been paid and balance is financed with monthly payment. Monthly payment will include interest expense also. So, to compute loan amount , present value of monthly payment will be calculated.To compute present value of monthly payment, interest rate will be calculated as discount factor.What will be the present value of monthly payment , is the loan amount.

Further, in case of annuity due, payment is made at the beginning of period. But, here, payment is made at the end of month.So, it an ordinary annuity not an annuity due.