Consider the following bonds:

$\backslash$table$[[$Bond$,$Coupon Rate $($annual payments$),$Maturity $($years$)],[$A$,0\%,16],[$B$,0\%,9],[$C$,6\%,16],[$D$,8\%,9]]$

a$.$ What is the percentage change in the price of each bond if its yield to maturity falls from $4\%$ to $3\%?$

b$.$ Which of the bonds $A-D$ is most sensitive to a $1\%$ drop in interest rates from $4\%$ to $3\%$ and why? Which bond is least sensitive$?$ Provide an intuitive explanation for your answer. Note Assume annual compounding

a$.$ What is the percentage change in the price of each bond if its yield to maturity falls from $4\%$ to $3\%?$

The percentage change in bond $A$ is $\%.($Round to two decimal places$)$

The percentage change in bond $B$ is $\%.($Round to two decimal places.$)$

The percentage change in bond $C$ is $\%.($Round to two decimal places.$)$

The percentage change in bond $D$ is $\%($Round to two decimal places.$)$

b$.$ Which of the bonds A through $D$ is most sensitive to a $1\%$ drop in interest rates, from $4\%$ to $3\%,$ and why? $($Select the best choice below.$)$

A$.$ Bond $A,$ because it has the lowest coupon and longest maturity

B$.$ Bond $B,$ because it has the lowest coupon and shortest maturity

C$.$ Bond C$,$ because it has the shortest maturity and is the coupon bond with the lowest coupon.

D$.$ Bond D$,$ because it has the highest coupon and shortest maturity.

Which of the bonds A through $D$ is least sensitive to a $1\%$ drop in interest rates, from $4\%$ to $3\%,$ and why? $($Select the best choice below.$)$

A$.$ Bond $A,$ because it has the lowest coupon and longest maturity.

B$.$ Bond $B,$ because it has the lowest coupon and shortest maturity.

C$.$ Bond $C,$ because it has the shortest maturity and is the coupon bond with the lowest coupon

D$.$ Bond D$,$ because it has the highest coupon and shortest maturity