Suppose a seven$-$year, $$1,000$ bond with a coupon rate of $8\mathrm{.}0\%$ and semiannual coupons is trading with a yield to maturity of $6\mathrm{.}75\%.$

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

b$.$ If the yield to maturity of the bond rises to $7\mathrm{.}00\%($APR with semiannual compounding$),$ what price will the bond trade for?

a$.$ Is this bond currently trading at a discount, at par, or at a premium? Explain. $($Select the best choice below.$)$

A$.$ Because the yield to maturity is greater than the coupon rate, the bond is trading at par.

B$.$ Because the yield to maturity is greater than the coupon rate, the bond is trading at a premium.

C$.$ Because the yield to maturity is less than the coupon rate, the bond is trading at a premium.

D$.$ Because the yield to maturity is less than the coupon rate, the bond is trading at a discount.