Your dreams of becoming rich have just come true. You have won the State of Tranquility's Lottery. The State offers you two payment plans for the $5,000,000 advertised jackpot. You can take annual payments of $250,000 for the next twenty years or $2,867,480 today.

a. If your investment rate over the next twenty years is 8%, which payoff will you choose?

b. If your investment rate over the next twenty years is 5%, which payoff will you choose?

c. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480?