Posting 2 subquestions as allowed per chegg's policy, please give detailed steps on both. Please show step by step workings without excel.

You have won the State'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. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480