Problem $4-54$ Calculating Annuities

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 $31$ annual payments of $$200,000,$ 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.

b$.$ You will receive $$615,000$ now, and you will not have to pay taxes on this amount. In

addition, beginning one year from today, you will receive $$150,000$ each year for $30$

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

Using a discount rate of $7$ 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$.,32\mathrm{.}16.)$

a$.$ Present value of Option A

b$.$ Present value of Option B