On April $1,$$$25,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $2\mathrm{.}05\%.$

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

$($b$)$ What is the yield rate on August $16$ if the market price is $$24,587\mathrm{.}74?$

$($c$)$ Calculate the market value of each $$25,000\mathrm{.}00$ T$-$bill on September $24$ if the rate of return on that

date is $3\mathrm{.}202\%.$

$($d$)$ What is the rate of return realized if a $$25,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on November

$6$ at a market rate of $3\mathrm{.}064\%?$