A $$1,000$ bond with a coupon rate of $6\mathrm{.}7\%$ paid semiannually has nine years to maturity and a yield to maturity of $6\mathrm{.}5\%.$ If interest rates fall and the yield to maturity decreases by $0\mathrm{.}8\%,$ what will happen to the price of the bond?

A$.$ The price of the bond will rise by $$56\mathrm{.}18.$

B$.$ The price of the bond will fall by $$56\mathrm{.}18.$

C$.$ The price of the bond will rise by $$78\mathrm{.}65.$

$$ D$.$ The price of the bond will fall by $$67\mathrm{.}42.$