Imagine that you have decided you need a new car, but not any car will do; you h
ID: 2700757 • Letter: I
Question
Imagine that you have decided you need a new car, but not any car will do; you have decided to purchase the car of your dreams. Conduct some research as to the cost of this car. You have determined in this imagined scenario that you could afford to make a 10% down payment. You can borrow the balance either from your local bank using a four-year loan or from the dealership%u2019s finance company. If you purchase from your dealership%u2019s finance company, the APR will be 10% with your 10% down and monthly payments over three years. However, the dealership will give you a rebate of 5% of the car price after the three year term is complete. You want the best deal possible, so you consider the following questions:
Explanation / Answer
The Chevy Camaro will cost $37,000 and the interest rate from USAA Bank will be 2.5% for a four year loan.
A 10% down payment would bring the price of the car down to $33,300.
37,000(.10) = 33,300
33,300(2.5/12)
(1 %u2013 (1 + 2.5 /12)-48)
33,300 (.21)
(1 %u2013 (1 + .21)-48)
6993
(1 %u2013 (1 + .21)-48)
33,300 + 6993 = 40,293
40,293/48 = 839.44
The payment for this car will be $839.44 monthly. The car would cost $40,293 in four years.
33,300 (10/12)
(1 %u2013 (1+10/12)-36)
33,300 (.83)
(1 %u2013 (1 + .83)-36)
27,639
(1 %u2013 (1 + .83)-36)
33,300 + 27,639 = 60,939
60,939/36 = 1,692.75
The payment for this car will be $1,692.75 monthly. The care would cost $60,939 in three years.
The 5% rebate of the car price, $60,939 would be $3,046.95 at the end of the three year term.
The better deal is the lower interest rate over the 4 year period. The car would be approximately $17,000 cheaper
What type of car have you selected, and what will it cost?
I selected a top of the line Jaguar, for the cost of $83,000
What is the interest rate from your local bank for a car loan for four years?
Interest rate is 3% for the four years.
What will your payment be to your local bank, assuming your 10% down payment? How much will that car have cost in four years?
The formula is [P(r/12)] / [1-((1=r/12)^-m
P( r/12) =74,700(3/12)^-48
(1-(1+3)/12) =.25
74,700(.25) =18,676
74,700 + 18,676 =$93,376
93,376/48= $1,945.33
My payment per month will be $1,945.33 and the car will cost $93,376.00 at the end of four years.
What will your payment be to the dealership finance company assuming your 10% down payment? How much will that car have cost in 3 years?
Dealership price at 10% down and the interest rate is at 10% for three years, with a 5% rebate at the end of three years.
The formula is [P(r/12)] / [1-((1=r/12)^-m.
P(r/12) = 74,700(10/12)
(1-(1+10/12)^-36) =.83
74,700(.83) =62,001
74,700+62,001 =136,701
136,701/36=3,797.25
My payment per month will be $3,797.25 and the car will cost $136,701.00 at the end of three years, however, with the 5% rebate at the end of the three years, I will get back $6,835.00. Therefore, I would pay $136,701 minus $6,835, which equal to $129,866.00(total)
Which is the better deal and why?
The better deal is the bank with the lower interest rate over 4 years. $129,866 is the car dealership%u2019s cost, minus $93,376 the bank%u2019s price, equal to $36,490, therefore, The car would be approximately $36,490 less expensive if I purchased it from the bank rather than the car dealership.