Problem $11\mathrm{.}4($a$)$

A $13\mathrm{.}25-$year maturity zero$-$coupon bond selling at a yield to maturity of $8\%($effective annual yield$)$ has convexity of $161\mathrm{.}9$ and modified duration of $12\mathrm{.}27$ years. A $40-$year maturity $6\%$ coupon bond making annual coupon payments also selling at a yield to maturity of $8\%$ has nearly identical modified duration$-12\mathrm{.}30$ years$$but considerably higher convexity of $272\mathrm{.}9.$

Suppose the yield to maturity on both bonds increases to $9\%.$ What will be the difference in actual percentage capital loss between the two bonds?

Problem $11\mathrm{.}4($b$)$

A $13\mathrm{.}25-$year maturity zero$-$coupon bond selling at a yield to maturity of $8\%($effective annual yield$)$ has convexity of $161\mathrm{.}9$ and modified duration of $12\mathrm{.}27$ years. A $40-$year maturity $6\%$ coupon bond making annual coupon payments also selling at a yield to maturity of $8\%$ has nearly identical modified duration$-12\mathrm{.}30$ years$$but considerably higher convexity of $272\mathrm{.}9.$

Suppose the yield to maturity on both bonds increases to $9\%.$ What is the difference between the two bonds in terms of the percentage capital gain predicted by the duration$-$with$-$convexity rule?