Suppose a seven$-$year, $\backslash (\backslash$$ $1,000\backslash )$ bond with a $\backslash (7\mathrm{.}8\backslash \%\backslash )$ coupon rate and semiannual coupons is trading with a yield to maturity of $\backslash (6\mathrm{.}34\backslash \%\backslash ).$

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 $\backslash (7\mathrm{.}35\backslash \%\backslash )($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 less than the coupon rate, the bond is trading at a discount.

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

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

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

b$.$ If the yield to maturity of the bond rises to $\backslash (7\mathrm{.}35\backslash \%\backslash )($APR with semiannual compounding$),$ what price will the bond trade for?

The new price of the bond is $\backslash (\backslash$$ $\backslash )$

$($Round to the nearest cent.$)$