Answer:
Kindly check explanation
Explanation:
Given the following :
Cost of house = $140,000
Down payment = $14000
Take back mortgage = 126000 = PV
Rate (r) = 5%
Yearly payment one can afford = 22000
a. If the loan was amortized over 3 years, how large would each annual payment be? Could you afford those payments?
Number of period = 3
Using the relation:
PMT = r(PV) / 1 - (1 + r)^-n
PMT = 0.05(126000) / 1 - 1.05^-3
PMT = 6300 / (1-0.8638375)
PMT = 46,268.23
He won't be able to afford it, as the monthly payment is larger than the affordable amount of $22000
b. If the loan was amortized over 30 years, what would each payment be? Could you afford those payments?
PMT = r(PV) / 1 - (1 + r)^-n
PMT = 0.05(126000) / 1 - 1.05^-30
PMT = 6300 / (1-0.2313774)
PMT = 8196.48
He would be able to afford it, as the monthly payment is lower than the affordable amount of $22000
c. To satisfy the seller, the 30-year mortgage loan would be written as a balloon note, which means that at the end of the third year, you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3, and what would the balloon payment be?
Present value of remaining balance after the 3rd year:
Present Value (PV) = PMT[(1 - (1 + r)^-n) / r]
Where
PMT = periodic payment = 8196.48
r = Interest rate = 5% = 0.05
n = number of periods = 30 - 3 = 27
PV = 8196.48[(1 - (1 + 0.05)^-27) / 0.05]
PV = 8196.48[(1 - (1. 05)^-27) / 0.05]
PV = 8196.48[0.7321516 / 0.05]
PV = 120,021.32
Balloon payment :
120,021.32 + 8196.48 = 128,217.80
