Newman Long has just learned he has won a $$514,700$ prize in the lottery. The lottery has given him two options for receiving the payments. $(1)$ If Newman takes all the money today, the state and federal governments will deduct taxes at a rate of $47\%$ immediately. $(2)$ Alternatively, the lottery offers Newman a payout of $20$ equal payments of $$36,400$ with the first payment occurring when Newman turns in the winning ticket. Newman will be taxed on each of these payments at a rate of $25\%.$

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Compute the present value of the cash flows for lump sum payout. $($Round answer to $0$ decimal places, e$.$g$.458,581.)$

Lump sum payout $

Assuming Newman can earn an $8\%$ 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, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.458,581.)$

Present value of annuity payout $

Which pay$-$out option should he choose?