https://file.aiquickdraw.com/mathbot/file/17278258000102yh3ai1h.jpg

To solve this problem, let’s break it down step by step:

### Information given:
- **Coupon bond par value:** $1,000
- **Annual coupon rate:** 10%
- **Annual coupon payment:** 10% of $1,000 = $100
- **Yield-to-maturity (YTM):** 10%
- **Time to maturity at purchase:** 12 years
- **Holding period:** 6 months (half-year)
- **Bond is sold after 6 months, with the same YTM of 10%.**

### Step-by-step solution:

1. **Initial bond price at purchase (Price at 12 years to maturity):**

   The bond price can be calculated using the present value of its coupon payments and the face value, discounted at the YTM of 10%. However, since the YTM matches the coupon rate, the bond will sell at par value, i.e., the price will be $1,000 when the bond is purchased.

2. **Coupon payment after 6 months:**

   Since the bond pays a 10% annual coupon and you are holding it for 6 months, you will receive half of the annual coupon. 

   \[
   \text{Coupon payment for 6 months} = \frac{100}{2} = 50 \text{ dollars}.
   \]

3. **Price of bond after 6 months (Price at 11.5 years to maturity):**

   After 6 months, the bond still has 11.5 years to maturity. However, since the yield-to-maturity remains 10%, and it’s a semi-annual coupon bond, the price will still be close to par ($1,000) after 6 months. This means the selling price of the bond will be approximately $1,000.

4. **Total return over the 6-month period:**

   You gain two things during the 6-month holding period:
   - A coupon payment of $50.
   - You sell the bond at $1,000, the same price at which you purchased it, so no capital gain or loss.

   The total return is the coupon payment divided by the initial bond price:
   \[
   \text{Total return} = \frac{50}{1000} = 0.05 \text{ or } 5\%.
   \]

Thus, the percentage return over the 6-month holding period is **0.0500**, or 5.00%.

Would you like further clarification or additional details?

---

Here are 5 related questions you might consider:
1. What would happen to the return if the bond was sold at a price above par value?
2. How does the duration of a bond affect its price sensitivity to interest rates?
3. How is the bond's price calculated if the YTM differs from the coupon rate?
4. What impact would an increase in interest rates have on your return in this scenario?
5. How would you annualize the 6-month return for comparison with other investments?

**Tip:** When evaluating bonds, always consider the impact of interest rate fluctuations on bond prices and yields.

A 10% coupon bond has a par value of $1,000 and a yield-to-maturity of 10%. You purchase the bond when it has exactly 12 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 hasn't changed when you sell it, what is your percentage return over this 6-month holding period? DO NOT annualize your answer. 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 over a 6-month holding period for a 10% coupon bond with a par value of $1,000. This problem explores key concepts such as bond valuation, yield-to-maturity, and percentage return calculations. Suitable for finance and economics students at the undergraduate level.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation