An investor purchased a $182-$day, $$25000$ T$-$bill on its issue date for $24639\mathrm{.}05$ After holding it for $69$ days, she sold the T$-$bill for a yield $2\mathrm{.}78\%$ of $($a$)$ What was the original yield of the T$-$bill? $($b$)$ For what price was the T$-$bill sold? $($c$)$ What rate of return $($per annum$)$ did the investor realize while holding this T$-$bill?