A 6% coupon bond has a par value of $1,000 and a yield-to-maturity of 8%. You purchase the bond when it has exactly 14 years remaining until maturity. You hold the bond for 6 months, collect the coupon payment, and then sell the bond immediately. If the bond's yield-to-maturity is 8% when you sell it, what is your percentage return over this 6-month holding period? Enter your answer as a decimal and show 4 decimal places. For example, if your answer is 6.25%, enter .0625.  Send with information in excel formulas  

To calculate your percentage return over the 6-month holding period, we need to follow a systematic approach. First, let's break it down into the components required:

1. **Coupon Payment**: Since the bond pays a 6% coupon annually and you hold it for 6 months, you receive half of the annual coupon.

2. **Price at Purchase and Sale**: Since the yield-to-maturity (YTM) remains constant at 8%, the price of the bond when you purchase it and sell it can be computed using the bond pricing formula.

### Step-by-step process:

#### 1. **Calculate the Price When You Purchase the Bond**  
   Use the bond pricing formula:
   \[
   \text{Price} = \sum_{t=1}^{n} \left( \frac{C}{(1 + r)^t} \right) + \frac{\text{Par Value}}{(1 + r)^n}
   \]
   Where:
   - $ C $ = Annual coupon payment = $ \frac{0.06 \times 1000}{2} = 30 $ (because you get it semi-annually)
   - $ r $ = Yield per period = $ \frac{0.08}{2} = 0.04 $
   - $ n $ = Total periods remaining = $ 14 \times 2 = 28 $ periods
   - Par Value = 1000

   The formula in Excel would be:
   ```excel
   = (30/(1+0.04)^1 + 30/(1+0.04)^2 + ... + 30/(1+0.04)^28) + 1000/(1+0.04)^28
   ```

   You can use the **PV** function in Excel for this:
   ```excel
   =PV(0.04,28,30,1000)
   ```

#### 2. **Price When You Sell the Bond**
   After 6 months, 13 years remain until maturity, so 26 periods remain. Use the same bond pricing formula but with 26 periods.

   In Excel, the price would be:
   ```excel
   =PV(0.04,26,30,1000)
   ```

#### 3. **Coupon Payment**
   You receive a coupon payment of $ 30 $ at the end of 6 months.

#### 4. **Calculate the Percentage Return**
   The return is based on the price difference plus the coupon payment received, divided by the initial price:
   \[
   \text{Return} = \frac{\text{Coupon Payment} + (\text{Price at Sale} - \text{Price at Purchase})}{\text{Price at Purchase}}
   \]

#### Example in Excel:
1. **Price at Purchase**:  
   ```excel
   =PV(0.04,28,30,1000)
   ```
2. **Price at Sale**:  
   ```excel
   =PV(0.04,26,30,1000)
   ```
3. **Return Calculation**:  
   ```excel
   = (30 + (Price at Sale - Price at Purchase)) / Price at Purchase
   ```

Now, I will calculate this step by step for you. Let me proceed with this.It seems I made an error with the calculation of periods at the time of sale. The number of periods should be an integer value. Let me fix that and recalculate.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can follow the steps I outlined earlier in Excel to calculate the percentage return. If you need further guidance, feel free to ask!

Here are the main steps for Excel:

1. **Price at Purchase**:
   \[
   =PV(0.04, 28, 30, 1000)
   \]
2. **Price at Sale**:
   \[
   =PV(0.04, 26, 30, 1000)
   \]
3. **Percentage Return**:
   \[
   = (30 + (Price\_at\_Sale - Price\_at\_Purchase)) / Price\_at\_Purchase
   \]

Would you like to explore these steps further or need assistance on a specific part?  

Here are 5 related questions to consider:
1. How would the return change if the YTM increased to 9%?
2. What would happen if the bond had only 5 years to maturity instead of 14?
3. How does the bond's price sensitivity relate to its YTM?
4. What if the coupon rate was higher, say 7%?
5. How does the holding period impact total return?

**Tip:** Understanding bond pricing and returns involves breaking down coupon payments, present value, and price changes—always approach it step by step!

A 6% coupon bond has a par value of $1,000 and a yield-to-maturity of 8%. You purchase the bond when it has exactly 14 years remaining until maturity. You hold the bond for 6 months, collect the coupon payment, and then sell the bond immediately. If the bond's yield-to-maturity is 8% when you sell it, what is your percentage return over this 6-month holding period? Enter your answer as a decimal and show 4 decimal places. For example, if your answer is 6.25%, enter .0625.

Learn how to calculate the percentage return on a 6% coupon bond with a par value of $1,000, held for 6 months, given an 8% yield-to-maturity. Follow a detailed step-by-step solution using bond pricing formulas and present value concepts. Suitable for finance students.

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