A $6-$month $$10,500$ treasury bill with a simple annual discount rate of $0\mathrm{.}47\%$ was sold in $2016.$ Assume $365$ days in a year.

$($a$)$ Find the price of the treasury bill $($T$-$bill$).$

$($b$)$ Find the actual interest rate paid by the Treasury.

$($a$)$ The price of the T$-$bill was $

$($Round to the nearest cent as needed.$)$