An investor purchased a $182-$day, $$$$10,000\mathrm{.}00$T$-$bill on its issue date for $ $9910\mathrm{.}29.$ After holding it for $136$days$,$ she sold the$$ T$-$bill for a yield of $1\mathrm{.}67\%.$

$($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?