$2.$ Interest Rate Risk $(15$ 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 $\backslash (2\backslash \%\backslash ).$ Consider this the baseline case for the $5-$year zero$-$coupon bond. $($b$)$ Calculate the price of the $10-$year zero$-$coupon bond when the yield of the bond $($quoted as an APR$)$ is $\backslash (2\backslash \%\backslash ).$ Consider this the baseline case for the $10-$year zero$-$coupon bond. $($c$)$ Calculate the price of the $5-$year zero$-$coupon bond when the yield of the bond $($quoted as an APR$)$ has decreased to $\backslash (1\backslash \%\backslash ).$ What is the price difference $($in percent$)$ compared to when the yield is $\backslash (2\backslash \%\backslash )?($d$)$ Calculate the price of the $10-$year zero$-$coupon bond when the yield of the bond $($quoted as an APR$)$ is $\backslash (1\backslash \%\backslash ).$ What is the price difference $($in percent$)$ compared to when the yield is $\backslash (2\backslash \%\backslash )?($e$)$ Calculate the price of the $5-$year zero$-$coupon bond when the yield of the bond $($quoted as an APR$)$ is $\backslash (3\backslash \%\backslash ).$ What is the price difference $($in percent$)$ compared to when the yield is $\backslash (2\backslash \%\backslash )?$

$($f$)$ Calculate the price of the $10-$year zero$-$coupon bond when the yield of the bond $($quoted as an APR$)$ is $\backslash (3\backslash \%\backslash ).$ What is the price difference $($in percent$)$ compared to when the yield is $\backslash (2\backslash \%\backslash )?$

$($g$)$ Describe the changes in bond prices $($in percentages$)$ you've calculated due to their maturity and changes in yields. For the same increase or decrease in yields, how do bond prices change depending on their maturity? With your answer, you're describing bond interest rate risk differences due to bond maturity.