3. An amortization is a method for repaying a loan by a series of equal payments, such as when a person buys a car or house. Each payment goes partially toward payment of Interest and partially toward reducing the outstanding principal. If a person borrows S dollars to buy a house, and if Pn denotes the outstanding principal after the nth payment of d dollars, then Pn satisfies the difference equation Pn+1= (1+1) Pn-d Po=S where I is the interest per payment period. a) Find Pn. b) Use the solution found in part (a) to find the payment d per period that must be made so as to pay back the dept in exactly N periods. c) Suppose you take out a $100.000 mortgage on a house from a bank that charges monthly interest of 1%. If the loan is to be repaid in 360 monthly payments (30 years) of equal amounts, what will be the amount of each payment?