1. Congratulations! You just won a lottery that will pay you $2,000 per week for the rest of your life! (Just FYI there are 52 weeks per year.) The payments start today, and will continue until your death. You expect that youll live for exactly 60 more years so you expect the very last payment to occur 60 years from now.

a. There are companies that buy lottery winnings they pay you a lump sum, and then they receive your lottery payments. How much are your expected lottery winnings worth, if you were to sell them today? Assume that your lottery winnings could have earned you 10% APR, compounded semi-annually.

b. You decide to sell your lottery winnings today at the value you calculated above. (If you cannot answer part (a), assume a value of $1 million.) You invest this money at 10% APR, compounded semi-annually, until you retire 30 years from now and this becomes your total retirement savings. Once you retire, you want your retirement savings to be able to pay a weekly CF, starting one week after you retire, for just the 30 years you plan on living in retirement, with nothing left after the 30 years. And you want your weekly CF to increase every week by 5.2% APR, compounded weekly. What would be your first retirement payment (occurring 1 week after you retire)?