A $10-$year Treasury bond pays $4\%$ interest semi$-$annually and has a par value of $$1,000.$ The yield to maturity is $6\%.$ If the yield to maturity declines to $5\%,$ what will happen to the market price of the bond?

Group of answer choices

Price decreases by $$72.$

Price decreases by $$50\mathrm{.}12$

Price increases by $$45\mathrm{.}98$

Price increases by $$70\mathrm{.}83.$