A bond has a par value of $1,000, a current yield of 8.03 percent, and semiannual coupon payments. The bond is quoted at 102.73. What is the coupon rate of the bond?

Multiple Choice

8.25%

16.50%

16.06%

8.03%

9.28%

To find the coupon rate of the bond, we can use the information given and calculate based on the following formula:

\[
\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Price of Bond}}
\]

Given dataTo find the coupon rate of the bond, we can use the information given and calculate based on the following formula:

\[
\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Price of Bond}}
\]

Given 
- **Par Value** = $1,000
- **Current Yield** = 8.03%
- **Price of Bond (Quoted Price)** = 102.73% of Par Value
- **Coupon Payments** = Semiannual

1. First, calculate the **Price of the Bond** in dollar terms:
   \[
   \text{Price of Bond} = 102.73\% \times 1000 = 1027.30
   \]

2. Rearrange the **Current Yield** formula to solve for the **Annual Coupon Payment**:
   \[
   \text{Annual Coupon Payment} = \text{Current Yield} \times \text{Price of Bond}
   \]
   \[
   \text{Annual Coupon Payment} = 0.0803 \times 1027.30 = 82.79
   \]

3. Now, the **Coupon Rate** is calculated as:
   \[
   \text{Coupon Rate} = \frac{\text{Annual Coupon Payment}}{\text{Par Value}} \times 100
   \]
   \[
   \text{Coupon Rate} = \frac{82.79}{1000} \times 100 = 8.28\%
   \]

Thus, rounding to match the provided answer choices, the closest option is **8.25%**.

### Final Answer:
**8.25%**

Would you like a breakdown of this approach, or have further questions?

---

1. How does a bond's price affect its current yield?
2. What is the difference between the current yield and the coupon rate?
3. How do semiannual coupon payments affect yield calculations?
4. What happens to the bond's current yield if the market price changes?
5. Why is the quoted price different from the par value?

**Tip:** Current yield provides a snapshot of annual income relative to the bond’s price, but it doesn’t account for the time value of money or capital gains/losses at maturity.

A bond has a par value of $1,000, a current yield of 8.03 percent, and semiannual coupon payments. The bond is quoted at 102.73. What is the coupon rate of the bond?

Determine the coupon rate of a bond with a $1,000 par value, a current yield of 8.03%, and semiannual coupon payments. Given that the bond is quoted at 102.73, learn how to apply yield and bond pricing formulas to find the coupon rate.

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