Bond Sam and Bond Dave both have $8$ percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. Bond Sam bond has four years to maturity, whereas the Bond Dave bond has $17$ years to maturity.

a$)$If interest rates suddenly rise by $2$ percent, what is the percentage change in the price 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$.,32\mathrm{.}16.)$

Percentage change in price of Bond Sam $\%$

Percentage change in price of Bond Dave $\%$

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

Percentage change in price of Bond Sam $\%$

Percentage change in price of Bond Dave $\%$