Final Answer:
The bond's coupon rate is 7.50%.
Step-by-step explanation:
The coupon rate of a bond represents the annual interest payment as a percentage of the bond's face value. In this case, we have a five-year, $1,000 bond selling at a price of $902.55 with a yield to maturity (YTM) of 6.5%.
Firstly, calculate the annual coupon payment using the YTM and the bond's price. The formula for yield to maturity is used to determine the discount rate that equates the present value of a bond's cash flows to its current price. By inputting the given values into the YTM formula and solving for the coupon payment, you can find it to be approximately $75.45.
Next, since the face value of the bond is $1,000, divide the annual coupon payment by the face value and then multiply by 100 to convert it into a percentage. So, $75.45 / $1,000 = 0.07545 * 100 = 7.545%.
Rounded to three decimal places, the bond's coupon rate is 7.50%. This rate signifies that the bond pays an annual interest of 7.50% of its face value, aligning with the given yield to maturity and current market price.