The winner of a lottery is awarded $$1,000,000$ to be paid in annual installments of $$50,000$ for $20$ years. Alternatively, the winner can accept a "cash value" one$-$time payment of $$450,000.$ The winner estimates he can earn $7\%$ annually on the winnings. What is the present value of the installment plan? $($Round your answer to two decimal places.$)$

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