You are negotiating the terms of a legal settlement. You have been given several different settlement options. Your average rate of return on the assets you currently hold is $6\mathrm{.}5\%$ and you expect to continue receiving that rate. You have a choice of receiving:

A lump sum today $(($:$t_0\}$ of $$40,000$ and payments of $$6,000$ at the end of the year for the next $6$ years $($total of $7$ payments$).$ Your total payout is $$76,000$ for the duration of the agreement.

Equal payments of $$9,C00$ for the next $9$ years at the beginning of each year $($total of $9$ payments$).$ Your total payout is $$81,000$ for the duration of the agreement.

Equal payments of $$13,000$ starting today and continuing annually for the next $5$ years $($total of $6$ payments$).$ Your total payout is $$78,000$ for the duration of the agreement.

a$)$ What is the present value of each alternative?

b$)$ Explain why receiving money today is better than receiving the same money later. Show work for all answers in excel.