Chad purchased a $90-$day interest$-$bearing note at $5\mathrm{.}00\%$ p$.$a$.$ that has a face value of $$10,000\mathrm{.}00.$

a$.$ If he holds the note for the full $90$ days, calculate the maturity value of the note.

Round to the nearest cent

b$.$ If the note is discounted $52$ days from maturity at a rate of $5\mathrm{.}60\%$ p$.$a$.,$ calculate his proceeds.

Round to the nearest cent

c$.$ In the short time Samuel held the note, what rate of interest did he earn?

$\%$

Round to $2$ decimal places