A $$5,000$ bond with a coupon rate of $5\mathrm{.}9\%$ paid semiannually has four years to maturity and a yield to maturity of $6\%.$ 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 fall by $$170\mathrm{.}99.$

B$.$ The price of the bond will fall by $$142\mathrm{.}49.$

C$.$ The price of the bond will rise by $$142\mathrm{.}49.$

$$ D$.$ The price of the bond will rise by $$199\mathrm{.}49.$