$[$Chapter $4\mathrm{.}2]$ Calculate the requested measures in parts $($a$)$ through $($f$)$ for bonds A and B $($assume that each bond pays interest semiannually$)$:Bond A Coupon $8\%$ Yield to maturity $8\%$ Maturity $($years$)2$ Par $$100\mathrm{.}00$ Price $$100\mathrm{.}000$Bond B $9\%8\%5$ $$100\mathrm{.}00$ $$104\mathrm{.}055($a$)$ What is the price value of a basis point for bonds A and B $[$Hint: Calculate the change in the price of the bond if the yield to maturity changes from $8\%$ to $8\mathrm{.}01\%.]?($b$)$ Compute the Macaulay durations for the two bonds.$($c$)$ Compute the modified duration for the two bonds.$($d$)$ Compute the approximate duration for bonds A and B using the shortcut formula by changing yields by $20$ basis points and compare your answers with those calculated in part $($c$)[$Hint: approximate duration $=+\_,$where y is the change in yield used to calculate the $()()$new prices, P$+$ and P$\_$ are the new prices when the yield decreases and increases by y$,$ and P$0$ is an initial price.$].($e$)$ Compute the convexity measure for both bonds A and B$.($f$)$ Compute the approximate convexity measure for bonds A and B using the shortcut formula by changing yields by $20$ basis points and compare your answers to the convexity measurecalculated in part $($e$).$