Chris Long has just learned he has won a $$513,300$ prize in the lottery. The lottery has given him two options for receiving the payments. $(1)$ If Chris takes all the money today, the state and federal governments will deduct taxes at a rate of $47\%$ immediately. $(2)$ Alternatively, the lottery offers Chris a payout of $20$ equal payments of $$36,900,$ with the first payment occurring when Chris turns in the winning ticket. Chris will be taxed on each of these payments at a rate of $25\%.$

Compute the present value of the cash flows for lump sum payout. $($Round answer to $0$ decimal places$)$

Lump sum payout:

Assuming Chris can earn a $9\%$ rate of return $($compounded annually$)$ on any money invested during this period, compute the present value of the cash flows for annuity payout. $($Round factor values to $5$ decimal places and final answer to $0$ decimal places$)$

Present value of annuity payout:

Which pay$-$out option should he choose? Annuity or Lump Sum