Problem $7-20$ Interest Rate Risk $[$LO$2]$

Bond $J$ has a coupon rate of $4$ percent and Bond $K$ has a coupon rate of $10$ percent. Both bonds have $12$ years to maturity, make semiannual payments, and have a YTM of $7$ percent.

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage price change of these bonds? $($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? $($Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

Answer is complete but not entirely correct.

$\backslash$table$[[$a$.$ Bond J$,-12\mathrm{.}28,\%$