Suppose a $5-$year, $$1,000$ bond with a coupon rate of $12\%$ and semiannual coupons is trading with a yield to maturity of $10\mathrm{.}59\%.$

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 $10\mathrm{.}75\%($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.

The bond is currently trading $($Select the best choice below.$)$

A$.$ at a discount because the coupon rate is greater than the yield to maturity.

B$.$ at a premium because the yield to maturity is greater than the coupon rate.

C$.$ at a premium because the coupon rate is greater than the yield to maturity.

D$.$ at par because the coupon rate is equal to the yield to maturity.

SOLVE BOTH PARTS A AND B