Consider the following bonds:

$\backslash$table$[[$Bond$,$Coupon Rate $($annual payments$),$Maturity $($years$)],[$A$,0\%,17],[$B$,0\%,9],[$C$,6\%,17],[$D$,7\%,9]]$

a$.$ What is the percentage change in the price of each bond if its yield to maturity falls from $5\%$ to $4\%?$

b$.$ Which of the bonds A$-$D is most sensitive to a $1\%$ drop in interest rates from $5\%$ to $4\%$ and why? Which bond is least sensitive$?$ Provide an intuitive explanation for your answer. Note: Assume annual compounding.