Both Bond Twain and Bond Brooks have $10$ percent coupons, make semiannual payments,

and are priced at par value. Bond Twain has $5$ years to maturity, whereas Bond Brooks has

$10$ years to maturity. If interest rates suddenly rise by $2$ percent, what is the percentage

change in the price of Bond Twain? Of Bond Brooks? If rates were to suddenly fall by $2$

percent instead, what would the percentage change in the price of Bond Twain be then? Of

Bond Brooks? $(6$ points$).$