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 $1,000,000 advertised jackpot. You can take annual payments of $25,000 at the end of the year for the next 40 years or $206,094 today. a.If your investment rate over the next 40 years is 14%, which payoff will you choose? b. If your investment rate over the next 40 years is 11%, which payoff will you choose? c. At what investment rate will the annuity stream of $25,000 be the same as the lump-sum payment of $206,094? a.If your investment rate over the next 40 years is 14%, what is the present value of the $25,000 annual payments today? $nothing(Round to the nearest dollar.)