nterest Rate Risk $(35$ points$)$ Analyze the change in bond prices when yields $($to maturity$)$ change for the following two bonds: $1)$ A $5-$year zero$-$coupon bond with $1000$ face $($par$)$ value $2)$ A $10-$year bond zero$-$coupon with $1000$ face $($par$)$ value. Assume investors are valuing cash flows semi$-$annually. $($a$)$ Calculate the price of the $5-$year zero$-$coupon bond when the yield of the bond $($quoted as an APR$)$ is $2\%.$ Consider this the baseline case for the $5-$year zero$-$coupon bond