Cindy is purchasing a house for $100,000. She pays a downpayment of 20%, and tak

Question

Cindy is purchasing a house for $100,000. She pays a downpayment of 20%, and takes a mortgage-backed loan for the remainder. It is a 10 year loan with monthly payments at 3% 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 25%? 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

Loan amount = (1-.2)*100000 = $80000

monthly rate = 3/12 = .25%

80000 = PM*PVIFA(.25,120)

80000 = PM*103.5618

PM = 80000/103.5618 = $772.4856

we can lump 12 month as 1 year

so PM for 1 year = 772.4856*12 = $9269.8272

PV = 9269.8272*PVIFA(25,10) = 9269.8272*3.5705

PV = $33097.91

including DOwn payument = 33097.91+20000= $53097.91

if we do not lump whole amount then,

PV = 772.4856*PVIFA(25/12,120) = 772.4856*43.9574 = $33956.458

including DOwn payument = 33956.458+20000= $53956.46

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