Question $3(10$ points$)$

You have recently won the super jackpot in the Vietnam Lottery. After reading the fine print,

you discover that you have the following two options:

Option One: You will receive $31$ annual payments of $$300,000,$ with the first payment

being delivered today. The income will be taxed at a rate of $28$ percent. Taxes will be

withheld when the checks are issued.

Option Two: You will receive $$810,000$ now, and you will not have to pay taxes on this

amount. In addition, beginning one year from today, you will receive $$250,000$ each

year for $30$ years. The cash flows from this annuity will be taxed at $28$ percent.

a$)$ Using a discount rate of $4\mathrm{.}95$ percent, which option should you select?

b$)$ At what discount rate would you be indifferent between these two options?

$($rounding to $4$ decimal places$)$