Morgan John has just learned he has won a $$2,800,000$ prize in the state lottery. He has two options for receiving the payments: $(1)$ If Morgan takes all the money today, the state and federal governments will deduct taxes at a combined rate of $40\%$ immediately. $(2)$ Alternatively, the lottery offers Morgan a payout of $20$ equal payments of $$199,900$ with the first payment occurring when Morgan turns in the winning ticket. Morgan will be taxed on each of these payments at a rate of $30\%.$ Assuming Morgan can earn an $6\%$ rate of return $($compounded annually$)$ on any money invested during this period.

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Compute the present value of the cash flows for the lump sum payout.

Lump sum payout $

Compute the present value of the cash flows for the annuity payout. $($Round factor values to $5$ decimal places, eg$.1\mathrm{.}25124$ and final answer to $0$ decimal places, eg$.458,581.)$

Present value of annuity payout

$

Which pay$-$out option should he choose?