$[$Chapter $4\mathrm{.}4]$ Answer the below questions for bonds A and B$.$ Bond A Bond B CouponYield to maturity Maturity $($years$)$ ParPrice $8\%9\%8\%8\%25$ $$100\mathrm{.}00$ $$100\mathrm{.}00$ $$100\mathrm{.}00$ $$104\mathrm{.}055($a$)$ Calculate the actual price of the bonds for a $100-$basis$-$point increase in interest rates. $($b$)$ Using duration, estimate the price of the bonds for a $100-$basis$-$point increase in interest rates.$($c$)$ Using both duration and convexity measures, estimate the price of the bonds for a $100-$basis$-$point increase in interest rates. $($d$)$ Comment on the accuracy of your results in parts b and c$,$ and state why one approximation is closer to the actual price than the other.$($e$)$ Without working through calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is $10\%$ rather than $8\%.$