A bond has a par value of \( \$ 1,000 \), a current yield of 7.01 percent, and semiannual coupon payments. The bond is quoted at 96.09 . What is the coupon rate of the bond?

To find the coupon rate of the bond, we can use the relationship between the current yield, the annual coupon payment, and the market price of the bond. The current yield is calculated as the annual coupon payment divided by the current market price of the bond. 1. First, determine the market price of the bond: - Since the bond is quoted at 96.09, its market price is \( \$ 1,000 \times 0.9609 = \$ 960.90 \). 2. Now, use the current yield formula: - Current Yield = \( \frac{Annual\ Coupon\ Payment}{Market\ Price} \) - Rearranging gives \( Annual\ Coupon\ Payment = Current\ Yield \times Market\ Price = 0.0701 \times 960.90 \approx \$ 67.35 \). 3. Since the bond pays semiannual coupons, the coupon payment every six months is: - \( \frac{67.35}{2} \approx \$ 33.68 \). 4. The annual coupon payment is double this amount, hence: - Annual Coupon Payment = \( 33.68 \times 2 \approx \$ 67.35 \). 5. Calculate the coupon rate: - Coupon Rate = \( \frac{Annual\ Coupon\ Payment}{Par\ Value} = \frac{67.35}{1000} \approx 0.06735 \) or \( 6.735\% \). Thus, the coupon rate of the bond is approximately **6.74%** (rounded to two decimal places).