Tony long has just learned he has won a $$508,300$ prize in the lottery. The lottery has given him two options for receiving the payments. $(1)$ If Tony takes all the money today, the state and federal governments will deduct taxes at a rate of $46\%$ immediately. $(2)$ Alternatively, the lottery offers Tony a payout of $20$ equal payments of $$39,600$ with the first payment occurring when Tony turns in the winning ticket. Tony 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