Both Bond Sam and Bond Dave have $7$ percent coupon bonds outstanding, with semiannual interest payments, and both are currently

priced at the par value of $$1,000.$ Bond Sam has five years to maturity, whereas the Bond Dave has $20$ years to maturity.

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage change in the price of each bond?

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 each bond?

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