On April $1,$ $$10,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $1\mathrm{.}91\%.$

$($a$)$ What is the price of each $$10,000\mathrm{.}00$ T$-$bill on April $1?$

$($b$)$ What is the yield rate on July $19$ if the market price is $$9,813\mathrm{.}45?$

$($c$)$ Calculate the market value of each $$10,000\mathrm{.}00$ T$-$bill on September $24$ if the rate of return on that date is $2\mathrm{.}75\%.$

$($d$)$ What is the rate of return realized if a $$10,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on December $16$ at a market rate of $2\mathrm{.}796\%$

$($a$)$ The price is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$