$.$ The BigFoot Corporation has two bond issues with information as follows $($as of $2015).$ Assume semi$-$annual interest payments and no arbitrage.

Bond A Bond B

Maturity $20272030$

Coupon $(\%)108$

Yield to maturity $(\%)9\mathrm{.}58$

Macaulay duration $($year$)5\mathrm{.}710$

Convexity $48100$

$4\mathrm{.}1$ Calculate price and modified duration for Bond A and Bond B$,$ respectively. Explain why modified duration is a better measure than maturity when calculating the bond$$ sensitivity to changes in interest rates.

$(8\%)$

$4\mathrm{.}2$ Calculate the approximate price change for Bond A and Bond B$,$ respectively, considering only duration, if the both yields increase by $300$ basis points.