$2.$a$.$ A semi$-$annual bond with a face $($par$)$ value of $$1,000$ has an annual coupon rate of $8\%.$ If $23$ days have passed since the last coupon payment, how much will be the accrued interest on the bond? What will be invoice price if the bond is selling at its par value?

b$.$ What will be the invoice price if the bond is a discount bond with a yield to maturity $($YTM$)$ of $10\%$ and a maturity of $10$ years?