You borrow $150,000 at 9% interest compounded monthly for 30 yearsto buy a new home. The monthly mortgage payment has been determinedto be $1206.94 (a) Find a recursive sequence that gives the balancebn of the mortgage remaining after each monthlypayment n has been made. (b) Use the table feature of a graphing utility to find the balance remaining for every five years where 0 < n<360 (c) What is the total amount paid for a $150,000 loan under these conditions? (d) How much interest will be paid over the life of the loan?