Bond J has a coupon rate of $5$ percent. Bond K has a coupon rate of $9$ percent. Both bonds have $8$ years to maturity, make semiannual payments, and have a YTM of $6$ percent.

If interest rates suddenly rise by $3$ percent, what is the percentage price change of Bond J$?$

multiple choice $1$

$-15\mathrm{.}27\%$

$-17\mathrm{.}25\%$

$-17\mathrm{.}27\%$

$-16\mathrm{.}27\%$

If interest rates suddenly rise by $3$ percent, what is the percentage price change of Bond K$?$

multiple choice $2$

$-13\mathrm{.}85\%$

$29\mathrm{.}77\%$

$-15\mathrm{.}83\%$

$-15\mathrm{.}85\%$

If interest rates suddenly fall by $3$ percent, what is the percentage price change of Bond J$?$

multiple choice $3$

$21\mathrm{.}78\%$

$-22\mathrm{.}47\%$

$21\mathrm{.}76\%$

$-17\mathrm{.}29\%$

If interest rates suddenly fall by $3$ percent, what is the percentage price change of Bond K$?$

multiple choice $4$

$19\mathrm{.}70\%$

$1\mathrm{.}00\%$

$19\mathrm{.}82\%$

$-15\mathrm{.}87\%$