Problem $7-20$ Interest Rate Risk $($LO$2)$

Bond J has a coupon rate of $7$ percent. Bond K has a coupon rate of $13$ percent. Both bonds have $15$ years to maturity, make semiannual payments, and have a YTM of $10$ percent.

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage price change of these bonds? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ What if rates suddenly fall by $2$ percent instead?

$$ Bond J: $\%$

$$ Bond K: $\%$