Problem $7-19$ Interest Rate Risk $[$LO$2]$

Both Bond Sam and Bond Dave have $10$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has $18$ years to maturity.

a$.$

If interest rates suddenly rise by $2$ percent, what is the percentage change in the price of Bond Sam and Bond Dave? $($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 Bond Sam and Bond Dave? $($Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$