The market price of a semi-annual pay bond is $965.48. It has 14.00 years to maturity and a coupon rate of 8.00%. Par value is $1,000. What is the yield to maturity?

To calculate the yield to maturity (YTM) for a semi-annual pay bond, we use the bond pricing formula:

\[
\text{Price} = \sum_{t=1}^{N} \frac{\text{Coupon Payment}}{(1 + \text{YTM}/2)^t} + \frac{\text{Par Value}}{(1 + \text{YTM}/2)^N}
\]

### Given dataTo calculate the yield to maturity (YTM) for a semi-annual pay bond, we use the bond pricing formula:

\[
\text{Price} = \sum_{t=1}^{N} \frac{\text{Coupon Payment}}{(1 + \text{YTM}/2)^t} + \frac{\text{Par Value}}{(1 + \text{YTM}/2)^N}
\]

### Given 
- **Market Price** ($ P $) = $965.48
- **Par Value** ($ F $) = $1,000
- **Coupon Rate** = 8.00%
- **Time to Maturity** = 14 years
- **Coupon Payment Frequency** = Semi-annual (2 times per year)

### Step-by-Step Calculation
1. **Coupon Payment**:
   Since the bond pays semi-annually, the coupon payment is half the annual rate:
   \[
   \text{Coupon Payment} = \frac{8\% \times 1,000}{2} = 40 \text{ USD (semi-annually)}
   \]

2. **Total Number of Periods**:
   Since the bond is semi-annual with 14 years to maturity:
   \[
   N = 14 \times 2 = 28 \text{ periods}
   \]

3. **YTM Calculation (Iterative Approach)**:
   The yield to maturity (YTM) is the rate $ r $ that satisfies the equation:
   \[
   965.48 = \sum_{t=1}^{28} \frac{40}{(1 + r/2)^t} + \frac{1000}{(1 + r/2)^{28}}
   \]
   Since this equation cannot be solved algebraically, we need to use either a financial calculator or numerical methods to estimate $ r $.

### Solution
Using trial and error or a financial calculator, we find:

\[
\text{YTM} \approx 8.36\% \text{ annually (or approximately 4.18% semi-annually)}
\]

### Final Answer
The yield to maturity for this bond is approximately **8.36% per year**.

Would you like a deeper breakdown of any steps or additional explanations?

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1. How would the YTM change if the bond price increased?
2. What is the difference between YTM and current yield?
3. How does a bond’s maturity affect its sensitivity to interest rate changes?
4. What if the bond paid interest annually instead of semi-annually?
5. How would the calculation adjust for a bond selling at a premium?

**Tip**: When calculating YTM, remember that semi-annual payments mean you should divide the coupon rate and YTM by 2, and double the years to maturity.

Calculate the yield to maturity (YTM) of a semi-annual pay bond with a market price of $965.48, 14 years to maturity, a coupon rate of 8%, and par value of $1,000. This finance problem covers core concepts in bond pricing and yield calculations, suitable for college-level finance students.

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