Both Bond Sam and Bond Dave have $11\mathrm{.}4$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has $5$ years to maturity, whereas Bond Dave has $22$ years to maturity. Both bonds have a par value of $1,000.$

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage change in the price 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$.$ If rates were to suddenly fall by $2$ percent instead, what would be the percentage change in the price of these bonds?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

Answer is complete but not entirely correct.

$\backslash$table$[[,$Bond Sam,Bond Dave$],[$a$.$ Percentage change in price,$14\mathrm{.}06,\%,7\mathrm{.}12x,\%$