$2.$ Calculate the requested measures in parts $($a$)$ through $($f$)$ for bonds A and B $($assume that each bond pays interest semiannually$)$:

Bond A Bond B

Coupon $8\%9\%$

to maturity $8\%8\%$

Maturity $($years$)25$

Par $$100\mathrm{.}00$ $$100\mathrm{.}00$

Price $$100\mathrm{.}00$ $$104\mathrm{.}055$

$($c$)$ Compute the modified duration for the two bonds.

$($Hint: Macaulay duration: Bond A $=1\mathrm{.}8875,$ Bond B $=4\mathrm{.}1542)$

$($d$)$ Compute the approximate duration Yield 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$).$ Please try to apply the equation provided below:

approximate duration $=$