You are purchasing a new home and need to borrow $250,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.25% APR, compounded monthly, for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay 2 points, they can offer you a lower rate of 6.0% APR, compounded monthly, for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points you will need to borrow an additional $5000 to cover points you are paying the lender.

a. Assuming that you pay the points and borrow from the mortgage lender at an APR of 6.0% compounded monthly, then what will your monthly mortgage payment be? Assume payments are made at the end of each month.

b. Assuming that you don't pay the points borrow from the lender at an APR of 6.25%, compounded monthly, then what will your monthly mortgage payment be? Assume payments are made at the end of each month.