Mortgage Cindy is purchasing a house for $129,000. She pays a downpayment of 10%

Question

Mortgage Cindy is purchasing a house for $129,000. She pays a downpayment of 10%, and takes a mortgage-backed loan for the remainder. It is a 15 year loan with monthly payments at 4% APR interest. What is the amount of her monthly payment? What is the present value of all her payments, including her downpayment if her discount rate is 20%? For this part of the question, you can lump all her payments for each year together, as if there were only one cashflow each year. The downpayment happens in year 0, and the first 12 monthly payments make up year 1, and so on.

Explanation / Answer

a) Principal amount= $129000-(129000*0.1) = $116100

Monthly payment = (R/12)PW/(W-1) = (.04/12)116100*(1+0.0033)180/((1+0.0033)180-1)

=0.0033*116100*1.8094/0.8094 = $865.13

b) Year 0= 25800

Year 1 = 9228.07

Year 2 = 9228.07

Year 3 = 9228.07

Year 4 = 9228.07

Year 5 = 9228.07

Year 6 = 9228.07

Year 7 = 9228.07

Year 8 = 9228.07

Year 9 = 9228.07

Year 10 = 9228.07

Year 11 = 9228.07

Year 12 = 9228.07

Year 13 = 9228.07

Year 14 = 9228.07

Year 15 = 9228.07

Present value of all payment including downpayment = $164,221.11

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