(a) Assume I won 100 million dollars in a lottery that pays installments of 20 million dollars a year for five years or a lump sum of less than 100 million dollars. If I take the installments, my first installment would come the day I claimed my winnings at the state lottery office. If I take the lump sum, I would receive that payment the day I claimed my winnings at the state lottery office. Assume that the interest rate is 5% per year. Calculate what the lump sum should be so that it would exactly equal the stream of installments. You must show and explain your work to be given credit for this assignment.

(b) How would your answer change if the first installment in the question above did not come until one year after I claimed my winnings. You must show and explain your work to be given credit for this assignment.