On April $1,$ $$100,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $2\mathrm{.}66\%.$

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

$($b$)$ What is the yield rate on July $13$ if the market price is $$97,320\mathrm{.}75?$

$($c$)$ Calculate the market value of each $$100,000\mathrm{.}00$ T$-$bill on October $18$ if the rate of return on that date is $3\mathrm{.}534\%.$

$($d$)$ What is the rate of return realized if a $$100,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on November $23$ at a market rate of $3\mathrm{.}85\%?$

$($a$)$ The price is $

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