Final answer:
The student's question is about calculating the purchase price and determining if a bond was bought at a premium or discount, using present value calculations and considering changes in market interest rates. A simplified example illustrates the process of bond valuation, showing how interest rates affect bond prices inversely.
Step-by-step explanation:
The question revolves around the concept of bond valuation, which involves calculating the present value of a bond's future interest payments and its redemption value at maturity. The student is asked to compute the purchase price of a bond, as well as determine if it was bought at a premium or discount. Additionally, the student needs to create a bond schedule reflecting these calculations.
To illustrate the concept clearly, let us consider a simpler example. A two-year bond issued for $3,000 with an interest rate of 8% pays $240 in interest annually ($3,000 × 8%). At maturity, the bond will repay the principal of $3,000 plus the last interest payment of $240. If the discount rate, which reflects the market interest rate, is also 8%, the present value of the bond's cash flows equals their face value. However, if the market interest rate increases to 11%, the present value would decrease, indicating the bond would trade at a discount. The calculations use the present value formula (PV = FV / (1 + r)^n).
In the scenario involving an interest rate hike to 12%, the bond becomes less attractive, and its price would have to be lowered to appeal to investors, resulting in the bond selling at a discount. The relationship between bond prices and market interest rates is inverse; as interest rates rise, bond prices fall, and vice versa.