The state$$ lottery's million$-$dollar payout provides for $$$$2$million$($s$)$ to be paid over $19$ years in $20$ payments of $ $100$ comma $000.$ The first $ $100$ comma $000$ payment is made$$ immediately, and the $19$ remaining $ $100$ comma $000$ payments occur at the end of each of the next $19$ years.

$($a$)$ If $8$ percent is the appropriate discount$$ rate, what is the present value of this stream of cash$$ flows?

$($b$)$ If $16$ percent is the appropriate discount$$ rate, what is the present value of the cash$$ flows?

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Part $1$

a$.$ If $8$ percent is the appropriate discount$$ rate, what is the present value of this stream of cash$$ flows?

$$$

$$

enter your response here$($Round to the nearest$$ cent.$)$

b$.$ If $16$ percent is the appropriate discount$$ rate, what is the present value of the cash$$ flows?

$$$

$$

enter your response here $($Round to the nearest$$ cent.$)$