$(10$ pts$)$ Today you purchase a $$10,000$ face value $T-$note that matures in five years.The coupon rate is $8\%,$ and the price quote is $110\mathrm{.}20.$ The last coupon payment was $120$ days ago, and the next coupon will be paid $60$ days later. What are the accrued interest AND the dirty price? Round your answers to $2$ decimal places. Show your calculation steps to receive full credits.

$-$Clean Price $=$ Quoted price

$-$ Dirty Price $=$ Clean price $+$accrued interest