$($Annuities$)$: You have recently won the super jackpot in the Washington State Lottery. On reading the fine print, you discover that you have the following two options: a$.$ You will receive $31$ annual payments of $$175,000,$ with the first payment being delivered one year from today. The income will be taxed at a rate of $28$ percent. Tax will be withheld when the checks are issued. b$.$ Beginning today, you will receive $$125,000$ each year for $30$ years. The cash flow from this annuity will be taxed at $28$ percent. You will also receive $$530,000$ at the end of year $30$ which you will not have to pay tax on this amount. Using a discount rate of $10$ percent, which option should you select? $(20$ points$)$