On April $1,$ $$25,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $3\mathrm{.}29\%.$

$($a$)$ What is the price of each $$25,000\mathrm{.}00$ T$-$bill on April $1?$

$($b$)$ What is the yield rate on August $1$ if the market price is $$24,394\mathrm{.}61?$

$($c$)$ Calculate the market value of each $$25,000\mathrm{.}00$ T$-$bill on October $18$ if the rate of return on that date is $3\mathrm{.}891\%.$

$($d$)$ What is the rate of return realized if a $$25,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on November $16$ at a market rate of $4\mathrm{.}125\%?$

$($a$)$ The price is $$24205\mathrm{.}81.$

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

$($b$)$ The yield rate is $\%.$

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