Jane made a down payment of 2000 dollars toward the purchase of a car. To pay the balance of the purchase price, she has secured a loan from her bank at the nominal rate of 5.5 percent per year compounded monthly. Under the terms of her finance agreement, she is required to to make payments of 230 dollars per month for 36 months.
a)
What is the cash price of the car? dollars (round your answer to the nearest cent).
b)
How much, in total, will Jane spend on interest charges? dollars (round your answer to the nearest cent.).

Question

Jane made a down payment of 2000 dollars toward the purchase of a car. To pay the balance of the purchase price, she has secured a loan from her bank at the nominal rate of 5.5 percent per year compounded monthly. Under the terms of her finance agreement, she is required to to make payments of 230 dollars per month for 36 months. 
a)
What is the cash price of the car?  dollars (round your answer to the nearest cent). 
b)
How much, in total, will Jane spend on interest charges?  dollars (round your answer to the nearest cent.).

dumbcow · Answer

a) price of car is present value of loan + down payment
monthly int rate = 5.5%/12 = .004583
v = 1/(1+i) = .9954375
$$PV = 230(v+v^{2}+...v^{36}) =230\frac{v(1-v^{36})}{1-v} =7,616.93$$
cash price of car = 9,616.93
to find interest she will have to pay add up all payments and subtract PV
230*36 = 8,280
8820 - 7616.93 = 663.07

anonymous · Answer

Apply the formula for Loan Pmt, => PVA = $7,616.93
a) Cash price for the car: $7,616.93 + 2.000 = $9,616.93
@dumbcow It's pretty much seems like just copy cat from your work :")