Darren purchased $$250000$ in $364-$day T$-$bills $315$ days before maturity to yield $2\mathrm{.}86\%.$ After holding it for $120$ days, Darren sold the T$-$bill for a yield of $3\mathrm{.}25\%.$

a$.$ How much did Darren pay for the T$-$bills?

b$.$ For how much did Darren sell the T$-$bills?

c$.$ What rate of return $($per annum$)$ did Darren realize on the investment?