What is the effect of receiving a full $1,000 at maturity if bonds are purchased at a discount?

Receiving the full $1,000 at maturity when bonds are purchased at a discount leads to a situation where the yield to maturity (YTM) will be higher than the current yield. When a bond is bought at a discount, the investor pays less than the face value (e.g., $1,000) and will receive the full face value at maturity. This difference between the purchase price and the maturity value contributes to increased returns.

The current yield is derived from the bond's annual coupon payment divided by its market price. However, when calculating the yield to maturity, one takes into account not only the annual coupon payments but also the capital gain associated with the bond (the difference between the purchase price and the maturity value). Since the bond was purchased at a discount, the capital gain increases the overall return, resulting in a yield to maturity that exceeds the current yield.

This reflects a fundamental principle in bond investment: a bond bought at a discount benefits the investor at maturity, generating a greater yield due to the capital appreciation of the bond's value. Thus, receiving a full $1,000 at maturity is critical in elevating the yield to maturity above the current yield.