Final answer:
The concept of bond premium and discount is related to the initial pricing of the bond compared to its face value. As a bond nears maturity, any premium or discount converges to zero due to the process of amortization. Calculations at a constant yield to maturity show this effect as the present value of future cash flows changes with the time to maturity.
Step-by-step explanation:
The question asks to demonstrate how a bond premium or discount diminishes as it approaches maturity, given a constant yield to maturity of 8%. The values for a bond with 7 and 2 years to maturity need to be calculated to show this effect. Here is an explanation of the underlying concepts and calculations:
Concept of Bond Premium and Discount
A bond issued at a price higher than its face value is said to be at a premium, while a bond issued at a price lower than face value is at a discount. A premium arises when the bond's coupon rate is higher than the prevailing market interest rates, and a discount arises when the coupon rate is lower.
Impact of Time to Maturity on Bond Pricing
The time to maturity has a significant impact on bond pricing. As the bond approaches maturity, any premium or discount slowly converges to zero, and the bond's price moves towards its face value. This process is called amortization of the premium or discount.
Calculations at Constant Yield to Maturity
The sales price of a bond can be found by discounting each future cash flow back to the present using the yield to maturity as the discount rate. These include the annual interest payments and the final principal repayment. The closer the bond is to maturity, the less impact the discounting has on the sales price.
Implications of a Constant Yield to Maturity
When the yield to maturity remains constant, the bond's price will decrease if it's trading at a premium or increase if it's trading at a discount. This is because the premium or discount is being amortized over the remaining lifespan of the bond.