Suppose a seven$-$year, $$1,000$ bond with a$($n$)5\mathrm{.}58\%$ coupon rate and semiannual coupons is trading with a yield to maturity of $2\mathrm{.}90\%.$

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 $2\mathrm{.}97\%($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 par because the coupon rate is equal to the yield to maturity.

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

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

b$.$ If the yield to maturity of the bond rises to $2\mathrm{.}97\%($APR with semiannual compounding$),$ at what price will the bond trade?

The bond will trade for $$.($Round to two decimal places.$)$