$(10$ points total$)$ Consider a bond with $$1000FV,$ an annual coupon rate of $6\%,$ an annual yield to maturity $($YTM$)$ of $10\%,$ and $10$ coupons remaining until maturity. Coupons are issued every $6$ months, and the next coupon is due in exactly $2$ months.

a$)(6$ points$)$ What is the CLEAN price of this bond today? $[$Assume all months are equal length. Show your work, and round your answer to $2$ decimal places $($eg$,456\mathrm{.}12).]$

Clean Price $=$$

b$)(4$ points$)$ Carefully explain why your calculated clean price in part a $($above$)$ is different than the price of this bond on the date of the last coupon payment. Your response should justify why the clean price is either higher or lower than the bond price on the last coupon date, assuming no difference in yield$-$tomaturity $($YTM$).$