Question

A new car is $20,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 5%/year compounded monthly. (Round your answers to the nearest cent.)

(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 72 months?

36 months	$
72 months	$

(b) What will the interest charges be if she elects the 36-month plan? The 72-month plan?

36-month plan	$
72-month plan	$

Answer 1

Given

     new car price =20,000

     down payment = 25% of 20,000 = 5000

      interest rate = 5% /year compounded monthly

a) monthly payment she has to make if car is financed over 36 months

    Total she has to pay at the end of 36 months = 15000*(1+5%/12)^(12*3) = 17422.08 ---->(1)

     Thus each month she has to pay 17422.08/36 = 483.94

monthly payment she has to make if car is financed over 72 months

    Total she has to pay at the end of 36 months = 15000*(1+5%/12)^(12*6) = 20235.26 ------>(2)

     Thus each month she has to pay 20235.26/72 = 281.04

b) from equation 1 Interest charges if she elects 36 months = 17422.08 -15000 =2422.08

    from equation 2 Interest charges if she elects 72 months = 20235.26 -15000 =5235.26