In 2004, a Massachusetts woman won 5.6 million dollars in the lottery, which would have paid her an initial gross payment of $283, 770 and 19 more yearly payments of $280,000 each (the first payment is at time 0 and the other payments occur at 1, 2, 3, .., 19). The only issue was that the winner, Louise Outing, was 94 years old at the time. "In March, I will be 95 years old. Do you realize that? Ninety-five in March...Now, you know I'm not going to live 20 years." the Everett woman said in a telephone interview. She wants the Massachusetts State Lottery Commission to cut her a check immediately for the full exist5.6 million, minus taxes. But the commission has so far rejected that request, saying Megabucks winners get 20-year annuities, not lump-sum payments. Ticket sales were 4 million dollars. Assume an interest rate of 10%.
a. Assuming that the payments are made over 20 years, how much money the lottery commission will have in their bank immediately after the last payment of $280,000?
b. If the commission had decided to pay Ms. Outing a lump sum at that time, how much would that be (before-tax amount)?