Suppose you buy a 1 million dollar house with a 20% deposit and pay off $b per fortnight. The following recurrence calculates the mortgage after n fortnights Xn = Xn-1 +0.002178Xn-1-b where Xn denotes the dollar amount of the loan after n fortnights, and assumes the (current) national average 30-year fixed mortgage APR (yearly rate) of 5.820%. (a) What is the initial loan X? (b) Determine the fixed points of this recurrence, and interpret these in terms of the loan and repayments. = (c) For repayments of b 2000, b = 3000, and b = 4000, determine the number of fortnights required for the loan to be payed off (i.e. the minimum value of n for which X 0) and the total amount payed. What can you conclude about the best way to pay off a loan?