Suppose a $3-$year, $$$$1,000$ bond with a $6\mathrm{.}17\%$ coupon rate and annual coupons is trading with a yield to maturity of $4\mathrm{.}40\%.$

a$.$ Is this bond currently trading at a$$ discount, at$$ par, or at a$$ premuim? Explain.

b$.$ If the yield to maturity of the bond rises to $5\mathrm{.}07\%($with annual$$ coupons$),$ at what price will the bond$$ trade?