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 $4$ percent? Alysha should pick A$)$ Payment at the end of each year or B$)$ Immediate Payment? 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.$)$