On April$1,$$$100$ comma $000\mathrm{.}00364-$day treasury bills were auctioned off to yield $3\mathrm{.}05\%.$

$($a$)$ What is the price of each $$$$100$ comma $000\mathrm{.}00$T$-$bill on April$1?$

$($b$)$ What is the yield rate on August $9$ if the market price is $$$$97$ comma $328\mathrm{.}17?$

$($c$)$ Calculate the market value of each $$$$100$ comma $000\mathrm{.}00$T$-$bill on September $16$ if the rate of return on that date is $3\mathrm{.}314\%.$

$($d$)$ What is the rate of return realized if a $$$$100$ comma $000\mathrm{.}00$T$-$bill purchased on April $1$ is sold on November $23$ at a market rate of $3\mathrm{.}327\%?$