Jack financed his new house with a mortgage for $100,000 amortized over 30 years for a five-year term @ 6% compounded monthly. Due to cicumstances beyond his control, Jack was forced to sell his house after 2 years, as well as the remaining balance of his mortgage at 4% compounded monthly. What was the price that Jack got for his mortgage? Help please. Thanks.
1- We have to find Jack's monthly payment. Using well-known formula for a loan payment, we get: $599.55
2-We have to find the mortgage balance after 2 years by using amortization, which comes to: $97,468.26.
3-We also need the mortgage balance at the end of its 5-year term, because the price will be based on that. By using amortization, the balance of the mortgage after 5 year will be:$93,054.37
4-We have to find the PV of the balance of the mortgage in (3) above, for the remaining 3 years using the well-known formula @ 4%, which comes to:$82,548.29.
5-Now, we have to find the PV of the stream of remaining 36 monthly payments of $599.55 each, using the well-known TVM formula @ 4%, which comes to:$20,307.22.
6-Finally, we add the two PV's in (4) and (5) together to get the sale price of the mortgage:
$82,548.29 + $20,307.22=$102,855.51-which is the price that Jack should get for his mortgage.
