You have recently won the super jackpot in the Washington State Lottery. After reading the fine print, you discover that you have the following two options:

a$.$

You will receive $30$ annual payments of $$150,000,$ with the first payment being delivered today. The income will be taxed at a rate of $30$ percent. Taxes will be withheld when the checks are issued.

b$.$

You will receive $$600,000$ now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $$100,000$ each year for $29$ years. The cash flows from this annuity will be taxed at $30$ percent.

Using a discount rate of $6$ percent, what is the present value of your winnings for each option? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$