Laurel, Inc., and Hardy Corp. both have $8$ percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $$1,000.$ The Laurel, Inc., bond has three years to maturity, whereas the Hardy Corp. bond 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? $($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? $($Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$