You're given with a mortgage from your credit union to buy a house that costs $640,000. Suppose you pay $128,000 for down payment and the current average market interest rate is 2.6% for the 15-year mortgage. Answer the following questions:

a)What is the monthly payment if there is no pre-payment penalty?

b)Suppose the credit union says that if you'd like to retire the loan earlier, say at the end of the 7th year, you need to pay (say) $348,000 for the rest of the loan, would you take it given that you have no difficulty to generate the cash flow? Why or why not?

c)Suppose that the credit union also offers you another possible payment program that is they will give you a low 1.2% interest rate for the first 6 years and with a lump-sum payment at the end of the 6^th year as $548,000. (The lump-sum payment is a one-time payment that you must pay it off or, you need to re-finance by then.) What is your monthly payment for the first 5 years?

d)Suppose you follow the original mortgage in (a) without any refinancing or prepayment, and after 5 years of payments, you discover the current market interest rate for mortgage drops to 1.8% APR. Instead of paying off the mortgage, you are about to re-finance your mortgage for 15-year mortgage instead. What is your monthly payment for your mortgage now? Is re-financing good for you?