Suppose Kyoko wants to earn a return of $13\mathrm{.}50$ percent and is offered the opportunity to purchase a $$1,000$ par value bond that pays a $15\mathrm{.}75$ percent coupon rate $($distributed semiannually$)$ and has three years remaining to maturity.

Use the following table to fill in values for the bond's coupon payment and present value, and Kyoko's semiannual required rate of return for this investment.

Variable Name

Coupon Payment

Semiannual Required Rate of Return

Present Value

Variable Value

$$78\mathrm{.}75$

$6\mathrm{.}7500$ percent

$$1,054\mathrm{.}05$

Now, suppose Kyoko wants to earn a return of $18\mathrm{.}00$ percent, but the bond being considered for purchase offers a coupon rate of $15\mathrm{.}75$ percent. It is a $$1,000$ par value bond that pays a $15\mathrm{.}75$ percent coupon rate $($distributed semiannually$)$ and has three years remaining to maturity, The bond's present value is $.,$ which is its par value, which means that the bond is

Given your calculations and conclusions, which of the following statements are true? Check all that apply.

When the coupon rate is greater than Kyoko's required rate of return, the bond should trade at a premium.

When the coupon rate is equal to Kyoko's required rate of return, the bond should trade at a premium.

When the coupon rate is equal to Kyoko's required rate of return, the bond should trade at a discount.

When the coupon rate is less than Kyoko's required rate of return, the bond should trade at a discount.