Q$2.$A bond with $20$ years to maturity, a coupon rate of $\backslash (4\backslash \%\backslash )$ paid quarterly, and a face value of $\backslash (\backslash$$ $1000\backslash )$ is currently trading at $\backslash (\backslash$$ $970\backslash ).$ a$)$ Calculate the bond's yield to maturity $($YTM$).$ b$)$ If you purchase this bond today and hold it for $7$ months $($receiving $2$ coupon payments during this time$),$ what would be the invoice price you would receive if you sell it one month after receiving the second coupon payment? c$)$ Calculate the Holding Period Return $($HPR$)$ as an Effective Annual Rate $($EAR$)$ for the $7$month investment period.