Suppose that a 30-year, nominal rate 8%, $100,000 mortgage payable monthly is to be refinanced at the end of 8 years for an additional 15 years at 6% with a refinancing closing cost amount of $1500 and 2 points. The points are each 1% of the refinanced balance including closing costs, and costs plus points are extra amounts added to the initial balance of the refinanced mortgage. Suppose that new pattern of payments is to be valued at each of the nominal interest rates 6%, 7%, or 8%, due to uncertainty about what the interest rate will be in the future and that these valuations will be taken into account in deciding whether to take out the new loan.

a) Suppose that you can forecast that you will in fact sell your house in precisely 5 more years after the time when you are refinancing. At the time of sale, you would pay off the cash principal balance, whatever it is. Calculate and compare the present values at each 6%, 7%, or 8% of your payments streams to the bank if:

(i) you continue the old loan without refinancing, and

(ii) if you refinance to get a 15-year 6% loan including closing costs and points