After hearing a knock at your front door, you are surprised to see the Prize Patrol from a large, well$-$known magazine subscription company. It has arrived with the good news that you are the big winner, having won $$23$ million. You have three options:

Receive $$1\mathrm{.}15$ million per year for the next $20$ years.

Have $$8\mathrm{.}75$ million today.

Have $$2\mathrm{.}75$ million today and receive $$850,000$ for each of the next $20$ years.

Your financial adviser tells you that it is reasonable to expect to earn $12$ percent on investments.

Required:

Calculate the present value of each option. $($Future Value of $$1,$Present Value of $$1,$ Future Value Annuity of $$1,$ Present Value Annuity of $$1.)$

Determine which option you prefer.