Answer the below questions for bonds A and $B.$

$\backslash$table$[[,$Bond A Bond B$],[$Coupon$,8\%,9\%,],[$Yield to maturity,$8\%,8\%,],[$Maturity $($years$),2,5,],[$Par$,$$$100\mathrm{.}00,$$$100\mathrm{.}00,],[$Price$,$$$100\mathrm{.}00,$$$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.