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.).

anonymous · Answer

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