Suppose a$$ seven$-$year, $$$$1$ comma $000$ bond with a coupon rate of $7\mathrm{.}5\%$ and semiannual coupons is trading with a yield to maturity of $6\mathrm{.}69\%.$

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 $7\mathrm{.}41\%($APR with semiannual$$ compounding$),$ what price will the bond trade$$ for?

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Part $1$

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 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 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.

Part $2$

b$.$ If the yield to maturity of the bond rises to $7\mathrm{.}41\%($APR with semiannual$$ compounding$),$ what price will the bond trade$$ for?

The new price of the bond is