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Morgan 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 $$20,540$ per year on June $30,$ beginning in $2029$ and continuing through $2032.$ To develop this fund, Morgan 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 Morgan to satisfy his objective? $($Round factor values to $5$ decimal places, eg$.1\mathrm{.}25124$ and final answer to $0$ decimal places, eg$.458,581.)$

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

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

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$($b$)$

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What are each of Morgan's contributions to the fund? $($Round factor values to $5$ decimal places, eg$.1\mathrm{.}25124$ and finalanswer to $0$ decimal places, e$.$g$.458,581.)$

Dargants contributions to the fund $

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