A bond manager is holding a $10-$year, $6\%$ coupon, option$-$free bond in his portfolio, he expects that interest will fall by $50$ basis points. He calculates that the bond price will change by $3\mathrm{.}63\%.$ if instead, rates rise by $50$ points, then the bond's price will change by:

A$.$Exactly $3\mathrm{.}63\%$

B$.$More than $3\mathrm{.}63\%$

C$.$Less than $3\mathrm{.}63\%$