6. 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.