A state lottery makes the following announcement: "Frederick Carbuncle has just won $100 million! We'll pay Frederick $10 million each year for the next 10 years!" a. Has Frederick really won $100 million? Explain. b. Many state lotteries allow winners to choose a single payment instead of a series of annual payments. "We'll offer you the present value of your annual payments, Frederick," the lottery commissioner says. "And because we're feeling generous, we'll use a really high interest rate when we calculate how much that prize will be. Congratulations, Fred!" Comment on the generosity of the lottery commissioner.