Your company currently has $

$1$

$,$

$000$

$$

par

$,$

$2\mathrm{.}25$

$\%$

$$ coupon bonds with

$10$

$$years to maturity and a price of

$.$

$

$1$

$,$

$080$

$$If you want to issue new

$$

$10$

$-$

year coupon bonds at

$$

$$par$,$ what coupon rate do you need to

$$

$$set$?$ Assume that for both

$$

$$bonds$,$ the next coupon payment is due in exactly six months.Suppose a seven$-$year, $$1,000$ bond with a $7\mathrm{.}5\%$ coupon rate and semiannual coupons is trading with a yield to maturity of $6\mathrm{.}61\%.$

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?

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 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 greater than the coupon rate, the bond is trading at a premium.

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