Question 1088989: In Spring 2010, some dealers offered a cash-back allowance of $1500 or 1.9% financing for 36 months on a Volkswagen Tiguan.
a) Determine the payments on a Volkswagen Tiguan if a buyer choose the
1.9% financing option and needs to finance $25,000 for 36 months,
compounded monthly.
Find the total amount the buyer will pay for this option.
b) Determine the payments on a Volkswagen Tiquan if a buyer chooses the
cash-back option and now needs to finance only $23,500. At the time, it was
possible to get a new car loan at 6.33% for 48 months, compounded monthly.
Find the total amount the buyer will pay for this option.
c) Discuss (write about) the pros and cons of each option. Give reasons for taking each.
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
In Spring 2010, some dealers offered a cash-back allowance of $1500 or 1.9% financing for 36 months on a Volkswagen Tiguan.
a) Determine the payments on a Volkswagen Tiguan if a buyer choose the
1.9% financing option and needs to finance $25,000 for 36 months,
compounded monthly.
Find the total amount the buyer will pay for this option.
b) Determine the payments on a Volkswagen Tiquan if a buyer chooses the
cash-back option and now needs to finance only $23,500. At the time, it was
possible to get a new car loan at 6.33% for 48 months, compounded monthly.
Find the total amount the buyer will pay for this option.
c) Discuss (write about) the pros and cons of each option. Give reasons for taking each.
Solution:
Refreshing to see a real-life problem!
Cash-back = $1500
Financing = 1.9% annual interest
Alternate financing = 6.33%
(a) monthly payment for 1.9% financing for 25000 over 36 months
A=25000(0.019/12)((1+0.019/12)^36)/((1+0.019/12)^36-1)
=714.97
Amount paid over life of loan = 714.97*36 = 25739.05
(b) monthly payment for 6.33% financing for $23500 over 48 months
=23500(0.0633/12)((1+0.0633/12)^48)/((1+0.0633/12)^48-1)
=555.46
Amount paid over life of loan = 555.46*48 = 26662.11
(c) Comments
The difference of total amount is not enormous (about 4%), but buyer can pay a lower monthly payment of $170 less per month. It all depends on the buyer's budget.
However, if the buyer decides to borrow for alternate source and amortized the loan over 36 months as well, then the monthly amount is $718.43, not even $4 a month more than the 1.9 finance option. This is probably why the financing option was 1.9%, not more, not less.
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