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.

To find the percentage return for the bond over a 6-month holding period, we will follow these steps:

### 1. **Coupon Payment Calculation**
   The bond pays a 6% annual coupon on a face value of $1,000. Since the bond pays semi-annual coupons (every 6 months):

   \[
   \text{Coupon Payment} = \frac{6\% \times 1,000}{2} = \frac{0.06 \times 1,000}{2} = 30
   \]

   So, the semi-annual coupon payment is $30.

### 2. **Price of the Bond at Purchase**
   Since the bond has 14 years to maturity and the yield-to-maturity (YTM) is 8%, we need to calculate the price of the bond at the time of purchase. The bond price is the present value of its future coupon payments and its face value discounted at the YTM. The YTM is 8% annually, or 4% semi-annually. Thus, the bond has 28 semi-annual periods remaining.

   The bond price can be calculated using the formula:

   \[
   \text{Bond Price} = \sum \left( \frac{C}{(1 + r)^t} \right) + \frac{\text{Face Value}}{(1 + r)^T}
   \]

   Where:
   - $ C = 30 $ (semi-annual coupon payment),
   - $ r = 0.04 $ (semi-annual YTM),
   - $ T = 28 $ (total semi-annual periods),
   - $ \text{Face Value} = 1,000 $.

   Therefore, the bond price at the time of purchase is:

   \[
   \text{Bond Price at Purchase} = 30 \times \sum \left( \frac{1}{(1.04)^t} \right) + \frac{1,000}{(1.04)^{28}}
   \]

### 3. **Price of the Bond at Sale**
   After 6 months, the bond has 13.5 years remaining to maturity, or 27 semi-annual periods. The YTM at the time of sale remains 8%. Therefore, the price of the bond at sale is calculated in a similar way as above, but with 27 periods remaining.

   \[
   \text{Bond Price at Sale} = 30 \times \sum \left( \frac{1}{(1.04)^t} \right) + \frac{1,000}{(1.04)^{27}}
   \]

### 4. **Total Return Over 6 Months**
   The total return over the 6-month period is composed of two parts:
   1. The coupon payment of $30.
   2. The capital gain or loss, which is the difference between the price at sale and the price at purchase.

   The percentage return over the 6-month period is given by:

   \[
   \text{Percentage Return} = \frac{\text{Coupon Payment} + (\text{Price at Sale} - \text{Price at Purchase})}{\text{Price at Purchase}}
   \]

We will now calculate the bond prices at purchase and sale using the formulas above. Let me proceed with that calculation.The bond's price at purchase is approximately \$833.3694, and the price at sale is approximately \$836.7041. 

The total return over the 6-month holding period is approximately **0.0400**, or **4.00%**.

Would you like further details or clarification?

Here are 5 related questions to explore further:
1. How does the bond's price change with varying yields to maturity?
2. What is the impact of holding a bond to maturity versus selling early?
3. How do changes in interest rates affect bond prices?
4. How are bond duration and yield to maturity related?
5. What role do coupon payments play in a bond's overall return?

**Tip:** Holding bonds longer exposes you to interest rate risks, but it also allows you to collect more coupon payments.

Learn how to calculate the percentage return over a 6-month holding period for a 6% coupon bond with a par value of $1,000 and a yield-to-maturity of 8%. This problem involves key financial concepts such as bond pricing, yield to maturity (YTM), and present value calculations, suitable for undergraduate finance or economics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation