An investor purchased a $182-$day, $$5000\mathrm{.}00$ T$-$bill on its issue date for $$4928\mathrm{.}81.$ After holding it for $79$ days, she sold the T$-$bill for a yield of $1\mathrm{.}64\%.$

$($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?