Consider the following two bonds that make semi$-$annual coupon payments. Assume the first coupon payment occurs in exactly six months, and the bond has a face value of $$1000.$

Coupon Rate Time to Maturity YTM

Bond A $3\mathrm{.}80\%8$ years $3\mathrm{.}6\%$

Bond B $3\mathrm{.}80\%18$ years $4\mathrm{.}2\%$

d$.)$ Use a spreadsheet to compute the annualized Macaulay duration and modified duration for Bond A at a yield$-$to$-$maturity of $3\mathrm{.}6\%.$ Provide an interpretation of the modified duration with regards to maturity and interest rate risk.

e$.)$ Use a spreadsheet to calculate the annualized convexity measure of Bond A at a YTM of $3\mathrm{.}6\%.$

f$.)$ Using the duration approximation formula with a convexity adjustment, what percentage change in the price of Bond A would you expect if the yield decreases by $150$ basis points?