Car Financing Project: Comparing Dealer Offers and Payments

This extra credit project for a finance course focuses on analyzing car financing options from four different dealerships. The student is tasked with calculating monthly payments, total amounts paid, and total interest paid for each dealer's offer, considering the loan amount, interest rate, and loan duration. The assignment requires the application of a specific formula to determine monthly payments and involves detailed calculations for each dealer's proposal. The student then compares the deals based on monthly affordability and the total interest incurred, ultimately recommending the most suitable option based on the financial situation of the borrower. The project emphasizes the importance of understanding loan terms and making informed decisions when financing a car. The solution demonstrates the calculations and provides a comparative analysis to determine the best financing option based on the given criteria.

Instructor: Prof. E. Palmer EXTRA CREDIT PROJECT
Show all work for full credit. Round decimals 3 places as they occur in each step. Round final
answers to whole numbers.
FINANCING A CAR
Advertisements for cars are bewildering. Suppose you have decided to purchase a car whose listed
price is $12,400. You have saved $2,000 to use as a down payment. After shopping around at several
dealerships, the offers available to you are given in the following table:
Dealer List Price Dealer
Discount
Down
Payment
Amount
Borrowed
Length of
Loan
APR (Annual
Rate of Interest
Dealer 1 $12,400 $1,000 $2,000 $9,400 3 years 3%
Dealer 2 $12,400 $1,000 $2,000 $9,400 5 years 6%
Dealer 3 $12,400 $1,500 $2,000 $8,900 4 years 5%
Dealer 4 $12,400 $1,500 $2,000 $8,900 3 years 4%
The first concern that you have is your monthly payment. The formula
can be used to compute your monthly payment . In this formula, is the amount borrowed, is
the monthly interest rate (in decimal form), where , is the length of the loan (in months).

1. Compute the monthly required by each dealer. (Show your work)
Dealer 1:
The monthly repayment is obtaibed using the firmula
where A=$ 9,400
i= 0.03
12 =0.003
n=12∗3=36
Now replacing the vakyes in the formula gives
M =9400∗( 1− ( 1+0.003 )−36
0.003 )
−1
=$ 276
Dealer 2:
The monthly repayment is obtaibed using the firmula
where A=$ 9,400
i= 0.06
12 =0.005
n=12∗5=60
Now replacing the vakyes in the formula gives
M =9400∗(1− ( 1+0.0 .005 )−60
0.005 )−1
=$ 182

Dealer 3:
The monthly repayment is obtaibed using the firmula
where A=$ 8,900
i= 0.05
12 =0.004
n=12∗4=48
Now replacing the vakyes in the formula gives
M =8900∗( 1− ( 1+0.004 ) −48
0.004 )
−1
=$ 204
Dealer 4:
The monthly repayment is obtaibed using the firmula
where A=$ 8,900
i= 0.04
12 =0.003
n=12∗3=36
Now replacing the vakyes in the formula gives
M =8,900∗( 1− ( 1+ 0.003 )−36
0.003 )
−1
=$ 261
2. What will be the total amount paid for the car under each dealer’s offer? (Show your work)

Dealer 1:
Total amount paid ¿ Down payment+(monthly payment∗number ofmonths)
¿ 2000+ ( 276∗36 ) =$ 11,936
Dealer 2:
Total amount paid ¿ Down payment+(monthly payment∗number ofmonths)
¿ 2000+ ( 182∗60 )=$ 12,920
Dealer 3:
Total amount paid ¿ Down payment+(monthly payment∗number ofmonths)
¿ 2000+ ( 204∗48 )=$ 11,792
Dealer 4:
Total amount paid ¿ Down payment+(monthly payment∗number ofmonths)
¿ 2000+ ( 261∗36 )=$ 11,396
3. What is the total amount of interest paid for the car under each dealer’s offer? (Show your work)
Dealer 1:
Interetst ¿ Total monthly payments− Amount borrowed
¿ ( monthly pay∗number of months ) −amount borrowed
¿ ( 276∗36 ) −9400=$ 536
Dealer 2:
Interetst ¿ Totalmonthly payments− Amount borrowed

¿ ( monthly pay∗number of months ) −amount borrowed
¿ ( 182∗60 )−9400=$ 1,520
Dealer 3:
Interetst ¿ Total monthly payments− Amount borrowed
¿ ( monthly pay∗number of months ) −amount borrowed
¿ 204∗48¿−8900=$ 892
Dealer 4:
Interetst ¿ Total monthly payments− Amount borrowed
¿ ( monthly pay∗number of months ) −amount borrowed
¿ ( 261∗36 )−8,900=$ 496
4. In conclusion, which do you think is the better deal? Why?
In selecting the most attractive deal will have to take the financial situation of the loanee into
consideration. Hence , in this analysis will look at two criteria; the amount the loanee is able to
pay per month and the total interest that will be incurred.
By looking at the amount payable per month, the best deal is the one offered by dealer 2. By
taking this deal the monthly instalment is just $182 which will be convenient for loanee who
does not have ahigh monthly income.
Looking at the total interest payable, the best deal is the one offered by dealer 4. By taking this
deal the loanee incur an interest of $ 496 which is the lowest out of all the 4 deals.
Hence should the loanee be able to pay the $261 needed monthly, I recommend taking this deal.