On April $1,$ $$100,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $1\mathrm{.}58\%.$

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

$($b$)$ What is the yield rate on August $23$ if the market price is $$98,791\mathrm{.}23?$

$($c$)$ Calculate the market value of each $$100,000\mathrm{.}00$ T$-$bill on October $9$ if the rate of return on that date is $2\mathrm{.}22\%.$

$($d$)$ What is the rate of return realized if a $$100,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on November $16$ at a market rate of $2\mathrm{.}583\%?$

$($a$)$ The price is $$.$

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