You want to purchase a house. The house costs $500,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price.

(a) The ABC bank offers a 30-year mortgage that requires annual payments and has an interest rate of 6% per year. What will your annual payment be if you sign up for this mortgage?

(b) Suppose you take the 30-year mortgage in part (a), how much will you still owe on the mortgage after 10 years?

(c) Assume now you are at the end of year 10, and you have just made your annual payment. You have decided to refinance your mortgage with a monthly payment of $3,000 with ABC bank at an interest rate of 5% p.a.. With this plan, how much earlier will you be able to pay off the mortgage?

(d) Assume there is another bank: BetterDeal Bank offer you another refinance option. It is still a monthly payment at $3,000 per month but with the interest rate at 5% p.a. compounding quarterly. Would you prefer this deal or the deal with ABC bank in part (c)? Explain.