On April $1,$ $$100,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $2\mathrm{.}50\%.$

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

$($b$)$ What is the yield rate on July $3$ if the market price is $$97,558\mathrm{.}97?$

$($c$)$ Calculate the market value of each $$100,000\mathrm{.}00T-$bill on September $10$ if the rate of return on that date is $3\mathrm{.}15\%.$

$($d$)$ What is the rate of return realized if a $$100,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on December $7$ at a market rate of $3\mathrm{.}48\%?$