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Alan Weatherspoon, a super salesman contemplating retirement on his fifty$-$fifth birthday, decides to create a fund on an $11\%$ basis

that will enable him to withdraw $$14,570$ per year on June $30,$ beginning in $2029$ and continuing through $2032.$ To develop this fund,

Alan intends to make equal contributions on June $30$ of each of the years $2025-2028.$

$($a$)$

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How much must the balance of the fund equal on June $30,2028,$ in order for Alan to satisfy his objective? $($Round factor values to $5$

decimal places, e$.$g$.125124$ and final answer to O decimal places, e$.$g$.458\mathrm{.}581)$

Balance of the fund equal on June $30,2028$ $

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$($b$)$

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