You just graduated and decided to buy a house. The house you like costs $210,000, and you plan to make a $10,000 down payment. You plan to pay for the house using equal monthly payments for 30 years and the best interest rate you can find is 6% compounded monthly. a) What is the payment? b) How much of your first payment goes to pay principal? c) The day your 180th payment is due, you win the lottery and decide to pay off the loan. What is the total amount you would owe the bank? d) (6 pts) How many payments would you need to make until over half the amount borrowed has been repaid? Do not interpolate. An estimate based on analysis is sufficient.