An eight percent (8%), twenty (20) year bond selling at a discount will have a:

When a bond is issued with a stated interest rate, also known as the coupon rate, and is selling at a discount, it means that the coupon rate is lower than the market interest rates. In this case, the bond's coupon rate is 8%, and because it is selling at a discount, the yield to maturity (YTM) will be higher than the coupon rate.

The yield to maturity reflects the total return an investor can expect to earn if the bond is held until maturity, accounting for the difference between the purchase price and par value, as well as the coupon payments. Since the bond is selling for less than its par value, the YTM will take into consideration this discount, leading it to be greater than the stated yield (or coupon rate) of 8%.

Therefore, it follows logically that the stated yield, which is based solely on the coupon payments, is less than the yield to maturity, as the YTM compensates for the bond's discount, resulting in overall higher returns for the investor if held to maturity.

This understanding illustrates why the relationship between the stated yield and the yield to maturity is crucial in bond valuation, especially under conditions where the bond is selling at a discount.