## Time value of money

1. I won 15 million dollars in a lottery that pays installments of 3 million dollars a year for five years or a lump sum of less than 15 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 6% per year.  Calculate what the lump sum should be so that it would exactly equal the present value of the stream of future payments.  You must show and explain your work to be given credit for this assignment. Assume there are no taxes on my winnings.
2. What would your answer change be 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.

I do not need pages of explanation.  Just three or four sentences for each question. However, I do need to see your work.