A $$1,000$ bond with a coupon rate of $7\%$ paid semiannually has ten years to maturity and a yield to maturity of $6\mathrm{.}2\%.$ If interest rates fall and the yield to maturity decreases by $0\mathrm{.}8\%,$ what will happen to the price of the bond?

A$.$ rise by $$88\mathrm{.}8$

B$.$ rise by $$63\mathrm{.}43$

C$.$ fall by $$76\mathrm{.}11$

D$.$ fall by $$63\mathrm{.}43$