You buy a 6% 1,000 bond for $1,000, immediately after semiannual interest has been paid to the previous owner. Eight years later, you sell the bond for $990.50, immediately after you received the semiannual interest check.  What is your yield during ownership?

To determine the yield during ownership of the bond, we'll need to calculate the bond's yield to maturity (YTM) considering the purchase price, the selling price, the interest payments, and the holding period.

Here's a step-by-step process to calculate the yield:

1. **Extract the given dataTo determine the yield during ownership of the bond, we'll need to calculate the bond's yield to maturity (YTM) considering the purchase price, the selling price, the interest payments, and the holding period.

Here's a step-by-step process to calculate the yield:

1. **Extract the given **
   - Purchase price of the bond ($P_0$): $1,000
   - Selling price of the bond ($P_f$): $990.50
   - Annual coupon rate: 6%
   - Face value of the bond ($FV$): $1,000
   - Holding period: 8 years
   - Coupon payments: semiannual, thus each payment is $ \frac{6\% \times 1,000}{2} = \$30$

2. **Calculate the total number of coupon payments received:**
   Since the bond pays interest semiannually and you held it for 8 years, the total number of coupon payments is:
   \[
   N = 8 \times 2 = 16 \text{ payments}
   \]

3. **Determine the total cash flows:**
   - Coupon payments: 16 payments of $30 each.
   - Final selling price: $990.50.
   - The total coupon payments received during ownership:
     \[
     16 \times \$30 = \$480
     \]

4. **Calculate the cash flows:**
   - Initial investment ($C_0$): $1,000 (cash outflow)
   - Coupon payments ($C_t$): $30 every six months for 16 periods (cash inflow)
   - Final cash flow ($C_f$): $990.50 (cash inflow at the end of the 8 years)

5. **Set up the cash flows for the yield calculation:**
   \[
   -1,000 + 30 \left( \frac{1 - (1 + r)^{-16}}{r} \right) + \frac{990.50}{(1 + r)^{16}} = 0
   \]

Here, $r$ is the semiannual yield. To solve this equation, we typically use a financial calculator or numerical methods due to its complexity. However, we can also use a financial calculator or an Excel spreadsheet to find the yield more conveniently.

Using an Excel spreadsheet, we can use the **IRR** (Internal Rate of Return) function to determine the yield:

### Steps in Excel:
1. Enter the cash flows into a column:
   - Cell A1: -1000 (initial investment)
   - Cell A2 to A17: 30 (coupon payments)
   - Cell A18: 1020.50 (last coupon payment + selling price)

2. Use the **IRR** function:
   - In a blank cell, enter: `=IRR(A1:A18)`
   - This will return the semiannual yield.

Suppose the result from Excel is $r = 2.92\%$.

3. **Convert the semiannual yield to an annual yield:**
   \[
   \text{Annual Yield} = (1 + r)^{2} - 1
   \]
   \[
   \text{Annual Yield} = (1 + 0.0292)^{2} - 1 = 0.0596 \text{ or } 5.96\%
   \]

Thus, your yield during ownership of the bond is approximately **5.96%** annually.

Would you like any details or have any questions about this calculation?

Here are 5 questions you might ask next:
1. How does changing the holding period affect the yield calculation?
2. What is the difference between yield to maturity and current yield?
3. How do market interest rates affect bond prices and yields?
4. Can you explain the impact of reinvestment risk on bond yields?
5. How do taxes affect the yield on a bond investment?

**Tip:** When calculating bond yields, using tools like financial calculators or Excel can greatly simplify complex calculations and provide accurate results quickly.

Learn how to calculate the yield during ownership of a 6% bond over 8 years. This problem involves bond valuation and yield to maturity calculations, considering a purchase price of $1,000, a selling price of $990.50, and semiannual coupon payments. Suitable for advanced learners and financial professionals.

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