Bond A $($semi$-$annual compounding$)$

Coupon $8\%$

Yield to maturity $10\%$

Maturity $($years$)10$

Par $$100\mathrm{.}000$

Price $$87\mathrm{.}5378$

$($a$)$ Calculate the actual price of the bond for a $100-$basis$-$point increase in interest rates.

$($b$)$ Using duration, estimate the price of the bond for a $100-$basis$-$point increase in interest rates.

$($c$)$ Using both duration and convexity measures, estimate the price of the bond for a

$100-$basis$-$point increase in interest rates.

$($d$)$ Without working through calculations, indicate whether the duration of bond A would

be higher or lower if the yield to maturity is $12\%$ rather than $10\%.$