A car dealer is offering to a buyer one of two incentives: zero percent financin

Question

A car dealer is offering to a buyer one of two incentives: zero percent financing or $3,000 cash back. If the car price (before the incentives) is $25,000, find the following to compare the two options in terms of monthly payments.

a. Financing through the dealer – Find the monthly payment to the car dealer for a $25,000 loan at zero percent interest for 5 years.         

b. Financing through a bank – Find the monthly payment to a bank for a 5 year loan at 6% when the buyer finances the $22,000 cost through a bank (i.e. the buyer takes the $3,000 cash back incentive).

Please read the questions carefully. Please draw the cash flow diagrams and explain the steps that you are going to approach to solve the problems then solve the problem. Show the details in solving the problems. Do not use excel or exponetnion equations, USE the method of...P=A(P/A,i,n)

Explanation / Answer

1) In this part the amount $25,000 is to be paid in 60 installments (60 months) with zero interest rate. First compute the future value of $25,000, which is, with no interest, is equivalent to $25,000. Now disburse it in 60 monthly installments. This implies a monthly payment of $417. (25000/60)

2) The loan amount is $22,000 at an interest rate of 6 perent for five years. First compute the future value of $22,000, which is, with 6 percent interest, is equivalent to

22,000(F/P, 6%, 5) = 22000*1.338 = $29436

This future value of $29,436 is to be paid in equal monthly installments with 0.5 percent montly interest rate. The monthly payment becomes: 29436(A/F, 0.5, 60) = 29436*0.0143 = $421 approximately.

Hence with the second option, the montly payment is $421.

Comparison reveals that the first option has a montly payment of $417 while the second option has a monthly paymemt of $421 with $3000 cash back. Hence the first option is more cost effective.

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