Both Bond Sam and Bond Dave have $11\mathrm{.}2$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has

$4$ years to maturity, whereas Bond Dave has $21$ years to maturity. Both bonds have a par value of $1,000.$

a$.$ If interest rates suddenly rise by $3$ 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 $3$ 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$.,32\mathrm{.}16.$