(10 pts) Shady Brian\'s Used Cars advertises a low 6% per year financing deal ov
ID: 2785282 • Letter: #
Question
(10 pts) Shady Brian's Used Cars advertises a low 6% per year financing deal over 24 months. Accordingly, Shady Brian offers the following deal on a lemon-yellow convertible ist pricc Less: Down Payment Balance to finance 5999.00 1500.00 4499.00 Add: Credit Investigation 6% of $4499 (269.94 per year) Total Monthly payment (total/24) 75.00 539.88 5113.88 213.08 Alternatively, Brian will sell you the car for $5250 now. Based on what you have learned from Dr. Leipzig, you realize this means that Shady Brian's deal is asking you to finance $5250 minus your down payment. What actual effective annual interest rate is paid on Shady Brian financing deal? For 5 points extra credit calculate the apparent effective annual interest rate that Brian is trying to trick you into considering.Explanation / Answer
Soln : Total amount in case if financing will be done = $5113.88 excluding the down payment.
In case if car is to but today at $5250, then payment excluding downpayment = 5250-1500 = $3750
t = 2 years n = no. periods = 12, r = 6%
Effective annual interest rate = (1+r/tn)^tn -1 = (1+0.06/24)^24 -1 = 6.18% i.e. actual effective interest rate
Now, again Brian is selling the car at upfront amount of 3750 +1500 = 5250,
Lets calculate the present value of 5113.88 = 5113.88/(1+r/n)^n = 3750
(1+r/24)^24 = 5113.88/3750
on calculating the value of r , we will get r = 31.22% , Apparent effective annual interest rate = 31.22%
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