You are thinking about buying a bond that offers a coupon rate of 6% but with semi-annual coupon payments. The bond has exactly 7 years remaining to maturity. The face value of the bond is $1,000. Your required return is 8.16% per year. How much should you be willing to pay for this bond?


To determine how much you should be willing to pay for this bond, we need to calculate its **present value** using the following approach. We'll break it down into two parts:

1. **Present Value of the Coupon Payments**: Since the bond offers semi-annual payments at a 6% annual coupon rate, the coupon payment per period is:
   \[
   \text{Coupon Payment} = \frac{6\% \times 1,000}{2} = 30 \text{ dollars every six months.}
   \]

2. **Present Value of the Face Value**: The face value of $1,000 will be paid back at maturity in 7 years (or 14 semi-annual periods).

Next, we'll use the **required return** (or discount rate) to calculate the present value of these future payments. Since the required return is 8.16% per year, the semi-annual required return is:
\[
\text{Semi-annual required return} = \frac{8.16\%}{2} = 4.08\%.
\]

### Formula for Bond Pricing:
The price of the bond (PV) is the sum of the present value of the coupon payments and the present value of the face value:
\[
PV = \sum \left( \frac{\text{Coupon Payment}}{(1 + \text{semi-annual required return})^t} \right) + \frac{\text{Face Value}}{(1 + \text{semi-annual required return})^{\text{total periods}}}
\]
Where:
- $ t $ is each semi-annual period (1 to 14)
- Total periods = 14 (7 years × 2)

Let me now calculate this for you.You should be willing to pay approximately **$886.52** for the bond, given your required return of 8.16% per year.

Do you need further explanation or details on this calculation? Here are some follow-up questions that expand on this concept:

1. How does the bond price change if the required return decreases to 7%?
2. What would happen to the bond price if the coupon rate were higher, say 8%?
3. How do changes in interest rates affect the price of bonds in general?
4. What is the difference between a bond's coupon rate and yield to maturity?
5. How does the concept of duration help in understanding bond price sensitivity?

**Tip**: The price of a bond is inversely related to the required rate of return; when interest rates rise, bond prices fall.

You are thinking about buying a bond that offers a coupon rate of 6% but with semi-annual coupon payments. The bond has exactly 7 years remaining to maturity. The face value of the bond is $1,000. Your required return is 8.16% per year. How much should you be willing to pay for this bond?

Learn how to calculate the price of a bond offering a 6% coupon rate with semi-annual payments and a maturity of 7 years. The face value is $1,000, and the required return is 8.16% per year. This finance problem involves present value concepts and bond pricing formulas. Suitable for college-level finance students.

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