What is the annual coupon rate of a ten-year bond trading at a price of 92.56% of par, if the yield is 6%? The coupon rate and yield follow the bond equivalent yield convention.

To determine the annual coupon rate of a bond, given its trading price and yield, we need to use the formula for the bond price. In this case, we use the present value formula for a bond, which accounts for both the present value of the coupon payments and the present value of the par value (face value) at maturity.

Here's how we can approach the solution:

### Given:
- Bond Price $ P = 92.56\% $ of par
- Yield to maturity $ YTM = 6\% $ (bond equivalent yield)
- Par value $ F = 100 $ (assuming par value of $100 for simplicity)
- Bond term $ n = 10 $ years

### Formula:

The price of the bond is given by the formula:
\[
P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n}
\]
Where:
- $ C $ is the annual coupon payment
- $ r $ is the yield to maturity per period (in this case, annually)

### Calculations:

1. **Convert the given price to a decimal:**
   \[
   P = 92.56\% \times F = 0.9256 \times 100 = \$92.56
   \]

2. **Using the bond pricing formula:**
   \[
   92.56 = \sum_{t=1}^{10} \frac{C}{(1 + 0.06)^t} + \frac{100}{(1 + 0.06)^{10}}
   \]

   To simplify, we need to calculate the present value of the par value at maturity:

   \[
   \text{Present value of par value} = \frac{100}{(1 + 0.06)^{10}} = \frac{100}{1.790847} \approx \$55.84
   \]

3. **Calculate the present value of coupon payments:**
   \[
   92.56 - 55.84 = 36.72
   \]

4. **Solving for C:**

   The present value of an annuity formula is used to find $ C $:

   \[
   36.72 = C \times \left( \frac{1 - (1 + 0.06)^{-10}}{0.06} \right)
   \]

   \[
   36.72 = C \times 7.36009
   \]

   \[
   C = \frac{36.72}{7.36009} \approx \$4.99
   \]

5. **Calculate the annual coupon rate:**
   \[
   \text{Coupon Rate} = \frac{C}{F} = \frac{4.99}{100} \approx 4.99\%
   \]

Therefore, the annual coupon rate of the bond is approximately **4.99%**.

**Would you like further details or have any questions? Here are some related questions you might be interested in:**

1. How do different types of yields affect the bond pricing?
2. What is the relationship between bond prices and market interest rates?
3. How does the bond equivalent yield differ from effective annual yield?
4. What are the factors influencing the yield to maturity of a bond?
5. How does a bond’s credit rating affect its price and yield?
6. What are the differences between a zero-coupon bond and a coupon bond?
7. How does bond duration relate to interest rate risk?
8. What is the impact of inflation on bond yields?

**Tip:** Understanding the relationship between bond prices and yields is crucial for making informed investment decisions.

Learn how to calculate the annual coupon rate of a bond trading at 92.56% of par with a 6% yield to maturity. Detailed step-by-step solution using bond pricing formulas and present value calculations.

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