A state lottery makes the following annoucement: "Fredrick Carbuncle has just won $$100$ million! We'll pay Fredrick $$10$ million each year for the next $10$ years!"

a$.$ Assuming the interest rate is strictly positive, in present value terms, Fredrick has won $$100$ million.

b$.$ Many state lotteries allow winners to choose a single payment instead of series of annual payments. "We'll offer you the present value of your annual payments, Fredrick," the lottery commisioner 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!"

The lottery commissioner's professions of generosity are genuine. True or False