Why does the yield on a discount security exceed the discount rate?

The yield on a discount security exceeds the discount rate because the yield reflects the total return an investor can expect upon maturity, which includes the difference between the purchase price and the face value. The discount rate, on the other hand, is simply the percentage reduction from the face value at which the security is sold. Since the yield accounts for the time value of money and the investment period, it typically appears higher than the nominal discount rate. This difference illustrates the actual profit an investor earns by holding the security until maturity.