A $13\mathrm{.}55-$year maturity zero$-$coupon bond selling at a yield to maturity of $8\%($effective annual yield$)$ has convexity of $169\mathrm{.}0$ and modified duration of $12\mathrm{.}55$ 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 $272\mathrm{.}9.$

Required:

a$.$ Suppose the yield to maturity on both bonds increases to $9\%.$

What will be the actual percentage capital loss on each bond?

What percentage capital loss would be predicted by the duration$-$with$-$convexity rule?

$($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

b$.$ Suppose the yield to maturity on both bonds decreases to $7\%.$

What will be the actual percentage capital gain on each bond?

What percentage capital gain would be predicted by the duration$-$with$-$convexity rule?

$($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$