Bond J has a coupon rate of $4$ percent. Bond K has a coupon rate of $10$ percent. Both bonds have $10$ 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 $1$

$-18\mathrm{.}73\%$

$-20\mathrm{.}71\%$

$-20\mathrm{.}73\%$

$-19\mathrm{.}73\%$

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

multiple choice $2$

$37\mathrm{.}54\%$

$-17\mathrm{.}92\%$

$-15\mathrm{.}92\%$

$-17\mathrm{.}90\%$

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

multiple choice $3$

$-32\mathrm{.}52\%$

$27\mathrm{.}56\%$

$-20\mathrm{.}75\%$

$27\mathrm{.}54\%$

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

multiple choice $4$

$7\mathrm{.}50\%$

$23\mathrm{.}38\%$

$-17\mathrm{.}94\%$

$23\mathrm{.}26\%$