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

Bond A Bond B

Coupon $8\%9\%$

Yield to maturity $8\%8\%$

Maturity $($years$)25$

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

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

Modified Duration $1\mathrm{.}8153\mathrm{.}994$

Convexity $4\mathrm{.}27719\mathrm{.}764$

$($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.

$($e$)$ Without working through calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is $10\%$ rather than $8\%.$

$6.$ State why you would agree or disagree with the following statement: When interest rates are low, there will be little difference between the Macaulay duration and modified duration measures.