Suppose that you would like to buy a house which costs $X. To finance the house, you consider paying with a fully amortized mortgage in 30 years. However, the interest rate is not fixed for entire life of the mortgage (adjusted rate mortgage). Instead, APR compounded monthly, for first 10 years is 7%, for years between 11 and 20 is 8% and finally for years between 21 and 30 is 9%. Given that the remaining balance at the end of 20th year is $100,000 (after the payment for that month is made), a) Find the cash flow and draw it. b) Find $X (present worth of the house)?