To calculate the percentage return on the bond over the 6-month holding period, we need to follow these steps:

Key Information:

• Coupon rate = 8% (annual)
• Par value = $1,000
• Remaining time to maturity = 11 years initially, but only 10.5 years after 6 months.
• Yield to maturity (YTM) when you sell the bond = 7% (annual)
• Holding period = 6 months

Steps:

1. Calculate the semi-annual coupon payment:
   The bond pays 8% annually on its par value of $1,000. The semi-annual coupon payment would be half of the annual coupon:

   $\text{Coupon payment} = \frac{8\% \times 1,000}{2} = \frac{80}{2} = 40 \text{ dollars}$

2. Calculate the price of the bond when you sell it:
   The price of a bond can be calculated using the formula for present value of future cash flows (coupon payments and face value at maturity) discounted at the yield to maturity (YTM). Since the bond will be sold after 6 months, there are 10.5 years left to maturity, and the yield to maturity is 7% annually (or 3.5% semi-annually).

   The price of the bond is the present value of the remaining coupons and the face value, calculated using the semi-annual YTM of 3.5%.

   The price of the bond is given by the formula:

   $P = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) + F \times (1 + r)^{-n}$

   Where:

   • $P$ = price of the bond
   • $C$ = semi-annual coupon payment ($40)
   • $r$ = semi-annual yield (3.5% or 0.035)
   • $n$ = number of remaining periods (21 periods left, as there are 10.5 years or 21 semi-annual periods)
   • $F$ = face value of the bond ($1,000)

   Substituting the values into the formula:

   $P = 40 \times \left( \frac{1 - (1 + 0.035)^{-21}}{0.035} \right) + 1,000 \times (1 + 0.035)^{-21}$

   First, calculate each part:

   • $(1 + 0.035)^{-21} \approx 0.48685$
   • $\frac{1 - 0.48685}{0.035} \approx 14.6843$

   Now calculate the bond price: $P = 40 \times 14.6843 + 1,000 \times 0.48685$ $P = 587.372 + 486.85 = 1,074.222$

   Therefore, the price of the bond when you sell it is approximately $1,074.22.

3. Calculate the total amount you receive during the holding period: During the 6-month holding period, you receive the coupon payment of $40. Upon selling the bond, you receive $1,074.22.

   So, the total amount received is: $\text{Total received} = 40 + 1,074.22 = 1,114.22$

4. Calculate the return over the holding period: The return is the percentage change in the value of the bond over the holding period. The initial value of the bond when purchased is $1,000, and the final value after the holding period is $1,114.22.

   The return is given by: $\text{Return} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}}$ $\text{Return} = \frac{1,114.22 - 1,000}{1,000} = \frac{114.22}{1,000} = 0.1142$

Thus, the return over the 6-month holding period is 0.1142 (or 11.42%).

Final Answer:

The percentage return over the 6-month holding period is 0.1142.

Let me know if you'd like more details or have any further questions!

Here are some related questions you might find useful:

1. How does the bond price change if the yield-to-maturity increases?
2. What is the effect of coupon rate on the bond price?
3. How do bond prices behave when interest rates change?
4. What would be the return if the bond were sold after one year instead of six months?
5. How do you calculate bond price using Excel or a financial calculator?

Tip: Remember that bond prices are inversely related to interest rates. When interest rates (or YTM) rise, bond prices fall.