On 5 October, someone in California bought the winning ticket for Powerball, whose prize was described as $699.8 million. The lucky winner gets 30 annual payments, the first payment now and the last payment 29 years from now. The amount of the payments increases by 5% per year. Assume inflation is 0%. a) What is the nominal value of the first payment? b) The present value of the jackpot is said to be $496 million. Given the nominal value of the first payment that you found in part a), what discount rate is implicitly being used? c) Suppose that Powerball changed its jackpot payment schedule to include a $100 million balloon payment in 29 years, with the remaining $599.8 million paid out as per above. Using the discount rate you found in b), what now would be the present value of the jackpot? d) Compare the PV in parts b) and c). If you find that they differ, then briefly explain why.