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 formula for the current yield of a bond: \[ \text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Bond Price}} \] Given: - Par value of the bond = $1,000 - Current yield = 7.01% - Semiannual coupon payments - Bond is quoted at 96.09 First, we need to calculate the annual coupon payment. Since the bond has semiannual coupon payments, the annual coupon payment is twice the semiannual coupon payment. Let's denote the semiannual coupon payment as \( C \). The annual coupon payment is \( 2C \). The current yield is given as 7.01%, so we can set up the equation: \[ 0.0701 = \frac{2C}{96.09} \] Now, we can solve for \( C \) and then find the coupon rate. Solve the equation by following steps: - step0: Solve for \(C\): \(0.0701=\frac{2C}{96.09}\) - step1: Divide the terms: \(0.0701=\frac{200C}{9609}\) - step2: Swap the sides: \(\frac{200C}{9609}=0.0701\) - step3: Convert the expressions: \(\frac{200C}{9609}=\frac{701}{10000}\) - step4: Multiply both sides of the equation by \(9609:\) \(\frac{200C}{9609}\times 9609=\frac{701}{10000}\times 9609\) - step5: Multiply the terms: \(200C=\frac{701\times 9609}{10000}\) - step6: Divide the terms: \(200C=\frac{6735909}{10000}\) - step7: Multiply by the reciprocal: \(200C\times \frac{1}{200}=\frac{6735909}{10000}\times \frac{1}{200}\) - step8: Multiply: \(C=\frac{6735909}{2000000}\) The semiannual coupon payment \( C \) is approximately $3.3679545. Since the annual coupon payment is twice the semiannual coupon payment, the annual coupon payment is \( 2 \times 3.3679545 = 6.735909 \). Now, we can find the coupon rate using the formula: \[ \text{Coupon Rate} = \frac{\text{Annual Coupon Payment}}{\text{Par Value}} \] Substitute the values: \[ \text{Coupon Rate} = \frac{6.735909}{1000} \] \[ \text{Coupon Rate} = 0.06735909 \] Therefore, the coupon rate of the bond is approximately 6.7359%.