Suppose a$$ seven$-$year, $$1,000$ bond with$$ a$($n$)7\mathrm{.}78\%7\mathrm{.}78\%$ coupon rate and semiannual coupons is trading with a yield to maturity of $5\mathrm{.}02\%.$

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 $5\mathrm{.}11\%($APR with semiannual$$ compounding$),$ at what price will the bond$$ trade?