On April $1,$ $$10,000\mathrm{.}00364-$day treasury bills were auctioned off to yield $2\mathrm{.}89\%$

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

$($b$)$ What is the yield rate on July $24$ if the market price is $$9,724,13?$

$($c$)$ Calculate the market value of each $$10,000\mathrm{.}00$ T$-$bill on October $16$ if the rate of return on that date is $3\mathrm{.}592\%.$

$($d$)$ What is the rate of return realized if a $$10,000\mathrm{.}00$ T$-$bill purchased on April $1$ is sold on December $12$ at a market rate of $3\mathrm{.}181\%?$