The purchasing power $P$ of a fixed income of $$30,000$ per year $($such as a pension$)$ after $t$ years of $5\%$ inflation can be modeled by

$P=30,000(1\mathrm{.}05{)}^{-t}.$

$($a$)$ Find the purchasing power after $5$ years. $($Round your answer to the nearest dollar.$)$

$($b$)$ Find the purchasing power after $20$ years. $($Round your answer to the nearest dollar.$)$

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