On April$1,$$$25$ comma $000\mathrm{.}00364-$day treasury bills were auctioned off to yield $2\mathrm{.}91\%.$

$($a$)$ What is the price of each $$$$25$ comma $000\mathrm{.}00$T$-$bill on April$1?$

$($b$)$ What is the yield rate on August $12$ if the market price is $$$$24$ comma $353\mathrm{.}74?$

$($c$)$ Calculate the market value of each $$$$25$ comma $000\mathrm{.}00$T$-$bill on September $19$ if the rate of return on that date is $3\mathrm{.}183\%.$

$($d$)$ What is the rate of return realized if a $$$$25$ comma $000\mathrm{.}00$T$-$bill purchased on April $1$ is sold on December $22$ at a market rate of $3\mathrm{.}582\%?$