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Steve, a super salesman contemplating retirement on his fifty$-$fifth birthday, decides to create a fund on a $11\%$ basis that will enable him to withdraw $$48,000$ per year on June $30,$ beginning in $2029$ and continuing through $2033.$ To develop this fund, Steve intends to make equal contributions on June $30$ of each of the years $2025-2028.$

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$($a$)$

How much must the balance of the fund equal on June $30,2029,$ in order for Steve to satisfy his objective? $($Round factor values to $5$ decimal places, es$.1\mathrm{.}25124$ and final answer to $2$ dedmal places, eg$.4,585\mathrm{.}81.)$

Balance of the fund equal on June $30,2029$$

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$($b$)$

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