An investor purchased a $91-$day, $$$$100,000\mathrm{.}00$T$-$bill on its issue date for $$99,373\mathrm{.}15.$ After holding it for $78$days$,$ she sold the$$ T$-$bill for a yield of $2\mathrm{.}11\%.$

$($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?

$$intructor tip:Yield is the r between the value on the given date and the maturity value.

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