Alysha has just won a lottery. She will receive a payment of $$3,000$ at the end of each year for $9$ years. As an alternative, she can choose an immediate payment of $$25,000.$

Which alternative should she pick if the interest rate is $8$ percent?

Alysha should pick

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What would the interest rate have to be for Alysha to be indifferent about the two alternatives? $($Round answer to $4$ decimal places, e$.$g$.25\mathrm{.}2341\%.$ Do not round your intermediate calculations.$)$

Interest rate