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 $2,000,000 advertised jackpot. You can take annual payments of $50,000 at the end of the year for the next 40 years or $666,585 today.

a.If your investment rate over the next 40 years is 9%, which payoff will you choose?

b. If your investment rate over the next 40 years is 5%, which payoff will you choose?

c. At what investment rate will the annuity stream of $50,000 be the same as the lump-sum payment of $666,585?