Final answer:
Petra's bond is trading at a premium since her purchase price exceeds the face value. Without precise details on the bond's payments, the coupon rate cannot be accurately determined. An example with a simple bond illustrates how present value and interest rates affect bond pricing.
Step-by-step explanation:
The subject of the question is concerned with whether Petra's bond, which she bought for $5,225.73 with a face value of $5,000 maturing in 6.5 years, is trading at par, premium, or a discount, and identifying the bond's coupon rate. Given the yield rate of 6.877%, we need to compare the purchase price of the bond to its face value.
A bond trading at par has a purchase price that is equal to its face value. If it is trading at a premium, the purchase price is higher than its face value. Conversely, if it is trading at a discount, the purchase price is lower than its face value. In the case mentioned, since the purchase price ($5,225.73) is higher than the face value ($5,000), the bond is trading at a premium.
Calculating the Coupon Rate
To determine the coupon rate, we should calculate the periodic interest payments and then express them as a percentage of the face value. However, without additional information, we cannot compute the coupon rate (r2) of this bond precisely. Typically, the coupon rate is determined by dividing the annual coupon payment by the face value of the bond.
Illustrating with an example of a simple two-year bond, let's consider if it were issued for $3,000 with an 8% interest rate. It would pay $240 in interest each year ($3,000 × 8%) and return the principal amount at the end of the term. To understand the bond's current worth or present value, we'd discount future payments by the current discount rate. For instance, with a discount rate of 8%, the present value would equal the sum of the future payments discounted back to the present, whereas if the discount rate increased to 11%, the present value would be lower.
Finally, considering the risk of the bond is essential. A risk-free bond would typically sell at its face value and pay the stipulated interest rate until maturity. If general market interest rates rise above the coupon rate of the bond, it may need to be sold at a discount below face value to attract buyers since they could earn a higher rate elsewhere.