Describe the relationship between the coupon rate and the required rate that will result in a bond selling at a premium?

To understand the relationship between the coupon rate and the required rate resulting in a bond selling at a premium, we need to first define a few concepts.

1. Coupon Rate: The coupon rate is the annual interest rate paid by the issuer of a bond to its bondholders. It represents the periodic interest payments that the bondholder will receive.

2. Required Rate: The required rate, also known as the yield to maturity (YTM), is the rate of return that investors demand for investing in a particular bond. It represents the annualized rate of return an investor expects to earn on a bond if it is held until maturity.

3. Bond Selling at a Premium: When a bond is selling at a premium, it means that the market price of the bond is higher than its face value. In other words, investors are willing to pay more than the bond's par value.

Now, let's consider the relationship between the coupon rate and the required rate for a bond to sell at a premium:

When the coupon rate is higher than the required rate, the bond is more attractive to investors because it offers a higher interest payment (coupon rate) compared to the return they require (required rate). As a result, investors are willing to pay more for the bond, driving its market price above its face value, and causing it to sell at a premium.

In summary, a bond will sell at a premium when its coupon rate is higher than the required rate, indicating that investors are willing to pay more for the bond due to the higher interest payments it offers relative to the required rate of return.