Suppose a$$ seven$-$year, $$$$1$ comma $000$ bond with a coupon rate of $7\mathrm{.}9\%$ and semiannual coupons is trading with a yield to maturity of $6\mathrm{.}47\%.$

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

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

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

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 less than the coupon$$ rate, the bond is trading at a discount.

Part $2$

b$.$ If the yield to maturity of the bond rises to $7\mathrm{.}42\%($APR with semiannual$$ compounding$),$ what price will the bond trade$$ for?

The new price of the bond is $$$$37\mathrm{.}1.($Round to the nearest$$ cent.$)$