Final answer:
The coupon rate of a five-year, $1,000 bond with a price of $898.61 and a yield to maturity of 6.4% is found by calculating the annual coupon payments that justify the bond's current price. Once the annual coupon payment is determined, it is divided by the bond's face value to find the coupon rate as a percentage.
Step-by-step explanation:
To calculate the coupon rate of a bond, we must consider the annual coupon payments, the price of the bond, and its face value. The yield to maturity (YTM) reflects the annual return on the bond if held until it matures. Given that we know the bond's price ($898.61), its face value ($1,000), its YTM (6.4%), and that it has annual coupons, we can find the coupon rate by setting up the equation for the present value of the bond that equates it to its price and solving for the coupon payment. The coupon rate is then calculated by dividing the annual coupon payment by the face value of the bond.
Using a financial calculator or a spreadsheet, we find the annual coupon payment that makes the present value of the coupon payments and the face value equal to the current price of the bond. Once we know the coupon payment, we can determine the coupon rate by dividing the annual coupon payment by the face value of the bond and converting it to a percentage.