6. (20 points) You plan to purchase a house for $500,000 in Stockton. You will make a down payment of 20% of the purchase price and borrow $400,000 from a local bank. The loan officer at the bank has provided you with several options which you want to evaluate very carefully. The options are (i) 30 -year fixed rate mortgage (FRM) at 7.2% per year with no discount point, (ii) 15 -year fixed rate mortgage (FRM) at 6.8% per year with no discount point, and (iii) 7/1,30-year adjustable rate mortgage (ARM) with no discount point. Under 7/1 ARM, the mortgage rate will be 4% per year for the first 7 years, but you expect the rate will go up to 9% during the 8th year. (a). Please determine the monthly mortgage payments for the options (i) and (ii). If you plan to prepay the remaining balance after 10 years of payment under option (i), how much would you have to pay at that time? How about under option (ii)? (b). Assume you have chosen option (i). If you wish to pay an additional $300 per month, how long would it take for you to pay off the mortgage? (c). If you obtain 7/1,30-year ARM under option (iii), what will be the monthly mortgage payment for the first 7 years? What will be your monthly payment during the 8th year