Find the clean and dirty price of a bond that pays coupons every $4$ months. The bond started on April $15,2017,$ and the valuation date is July $15,2022.$ The bond has a $12\mathrm{.}5\%$ interest rate, a face value of $$500,$ and is expected to be redeemed at $$580$ with a $12\%$ interest rate. Calculate for r$=8\%$ trimestral at January $18,2023.$