Suppose a $7-$year, $$1,000$ bond with a coupon rate of $9\%$ and semiannual coupons is trading with a yield to maturity of $7\mathrm{.}55\%.$

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 $7\mathrm{.}85\%($APR with semiannual compounding$),$ at what price will the bond trade?

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