A mortgage (loan for buying a house) is an ordinary annuity. With a standard 30-year fixed rate loan, the money is borrowed today and paid back monthly for 30 years in a constant amount. In Yolo County the maximum conforming loan amount is $552,000. A conforming loan meets conditions set by government sponsored entities (GSE) called Fannie Mae and Freddie Mac in the US. Conforming loans usually get a lower interest rate because the bank can sell them easily to the GSEs if they want.

a) Suppose someone borrows $552,000 today to buy a house in Davis, CA. If the annual interest rate is 4%, with monthly compounding, what should be the fair value monthly mortgage payment? Provide a calculation.

b) Banks will sometimes offer a homebuyer to "buy points". This allows the homebuyer to pay money to the bank today to lower the interest rate on their mortgage. One point is 1% of the borrowed amount. For example from part a), suppose 1 point would cost $5,520 and reduce the interest rate to 3.75%. Based on the new interest rate, what would be the monthly mortgage payment?

c) This is a tough question. Should the homebuyer take the deal from part b)? Provide a calculation. For any calculation that you do you should assume the annual interest rate is 4%.