Bond J has a coupon rate of $3$ percent. Bond K has a coupon rate of $9$ percent. Both bonds have $18$ years to maturity, make semiannual payments, and have a face value of $$1000$ and a YTM of $6$ percent.

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage price change of these bonds? What if rates suddenly fall by $2$ percent instead? $($Hint: $\%$ price change $=100\%*($new price $$ old price$)/$old price$)$

b$.$ What does this problem tell you about the interest rate risk of lower$-$coupon bonds?