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. Instead she sued the lottery commission for a lump-sum payment. Louise Outing is 94 years old, and she knew it would be foolish to expect to live another 20. So the lottery winner wants all of her cash now, not in payments spread out over the next two decades.(First payment is at the time of the claim and the other payments are 1, 2, 3, etc. from that time.) ''In March, I will be 95 years old. Do you realize that? Ninety-five in March," the Everett woman said in a telephone interview yesterday. ''Now, you know I'm not going to live 20 years. "Outing won the Sept. 4 Megabucks drawing, and she wants the Massachusetts State Lottery Commission to cut her a check immediately for the full $5.6 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. How much money the lottery commission will end up in their bank immediately after they pay the last payment of $280,000 to Ms. Outing. b. If the commission decide to pay Ms. Outing a lump sum, how much will that be? (Hint: initial payment plus the present value of the 19 payments).