Suppose you have won $200.000 in the state lottery, and you have decided to retire on your winnings. Suppose you deposit your winnings in a bank that pays 8% annual interest (compounded annually) and make yearly withdrawals of $30.000. (Hint: If periodic withdrawals, each of amount d, are deposited in a bank account whose initial amount is so that pays interest at a rate r per period, then the difference equation that describes the total amount Sn in the account after n periods is Sn+1=(1+r)Sn-d) a. What are the difference equation and initial condition that describes the future value of your account? b. Will you ever run out of money? If so, when? Suppose you have won $200.000 in the state lottery, and you have decided to retire on your winnings. Suppose you deposit your winnings in a bank that pays 8% annual interest (compounded annually) and make yearly withdrawals of $30.000. (Hint: If periodic withdrawals, each of amount d, are deposited in a bank account whose initial amount is so that pays interest at a rate r per period, then the difference equation that describes the total amount Sn in the account after n periods is Sn+1=(1+r)Sn-d) a. What are the difference equation and initial condition that describes the future value of your account? b. Will you ever run out of money? If so, when