Lottery. 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 $4,000,000 advertised jackpot. You can take annual payments of $80,000 at the end of the year for the next 50 years or $978,679 today. a. If your investment rate over the next 50 years is 10%, which payoff will you choose? b. If your investment rate over the next 50 years is 7%, which payoff will you choose? c. At what investment rate will the annuity stream of $80,000 be the same as the lump-sum payment of $978,679? a. If your investment rate over the next 50 years is 10%, what is the present value of the $80,000 annual payments today? $ (Round to the nearest dollar.)