Question

3. Cyrus decided to purchase a flat screen HDTV. He makes a down payment of $400 and secures financing for the balance of the purchase price at a rate of 14% /year compounded monthly. Under the terms of the finance agreement, he is required to make monthly payments of $125 for 30 months. (a) What was the cash price of the TV? N - PMT- FU= Vig-Ca (b) How much interest did Cyrus end up paying?

Answer 1

Part a: Cash Price of TV

Cash Price of TV = Downpayment + Loan Value

Downpayment = $ 400 .....Given

Loan Value = Needs to be calculated using PV function on excel or calculator as given below:

1.167% No. of Period Rate of Interest Future Value Monthly Payment Loan Value N i FV PMT PV Given = 14%/12 End of Loan Principal = 0 Given = PV(1.167%, 30, -125, 0, 0) 125 3149

Hence, Cash Price = 400 + 3149The abovementioned inputs can be used through a calculator as well and shall give the same answer.

Cash Price of the TV = $ 3,549 ... Answer

Note: In the image given, C/Y and P/Y have been mentioned. I would recomment not to use these functions and keep them at 1 as given in the image. Assuming these are set at 1, the abovementioned inputs should be used in the calculator.

Part b: How much interest did Cyrus end up paying

Monthly Installment: $ 125

No. of Installments = 30

Total Amount Paid = $ 125 * 30 = $ 3,750

This amount paid comprises of the interest and principal. The principal (loan value) borrowed was $ 3,149 as calculated in part a above.

Hence, Total Amount Paid = Principal Repaid + Interest Paid

$ 3,750 = $ 3,149 + Interest Paid

Interest Paid = $ 3,750 - $ 3,149

Interest Paid =  $ 601 .... Answer