You are thinking about buying a bond that offers an annual coupon rate of 6%, with exactly 8 years remaining to maturity. The face value of the bond is $1,000. Your required return is 5% 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 (PV)**. The bond's price is the sum of the present value of its coupon payments and the present value of its face value (par value) at maturity. Here's the step-by-step process:

### Given Data:
- **Coupon rate** = 6% per year
- **Annual coupon payment** = 6% of $1,000 = $60 per year
- **Face value** = $1,000
- **Time to maturity** = 8 years
- **Required return** = 5% per year

### Formula for bond pricing:

The price of the bond can be calculated as:

\[
\text{Price of bond} = \left( \sum_{t=1}^{8} \frac{\text{Coupon payment}}{(1 + r)^t} \right) + \frac{\text{Face value}}{(1 + r)^n}
\]

Where:
- $r$ is the required return (5%)
- $n$ is the number of years to maturity (8 years)
- Coupon payment is $60 each year

We will calculate the present value of the coupon payments and the present value of the face value separately.

### 1. Present Value of Coupon Payments:
This is the present value of an annuity, calculated as:

\[
PV_{\text{coupons}} = \text{Coupon payment} \times \left( 1 - \frac{1}{(1 + r)^n} \right) \div r
\]

\[
PV_{\text{coupons}} = 60 \times \left( 1 - \frac{1}{(1 + 0.05)^8} \right) \div 0.05
\]

### 2. Present Value of Face Value:
This is the present value of a lump sum, calculated as:

\[
PV_{\text{face}} = \frac{\text{Face value}}{(1 + r)^n}
\]

\[
PV_{\text{face}} = \frac{1,000}{(1 + 0.05)^8}
\]

Let me calculate these two values.The price you should be willing to pay for the bond, given a required return of 5%, is approximately **$1,064.63**.

Would you like more details on how the present values were calculated, or do you have any further questions?

Here are 5 related questions to expand on this concept:
1. How would the bond price change if the required return was 6% instead of 5%?
2. What is the effect of increasing the time to maturity on the bond's price?
3. How does the coupon rate influence the price of a bond relative to its required return?
4. What happens to the bond price if it is a zero-coupon bond?
5. How is yield to maturity (YTM) related to the bond price?

**Tip:** The bond price is inversely related to the required return (discount rate). As required returns rise, bond prices fall, and vice versa.

Learn how to calculate the price of a bond with a 6% coupon rate, 8 years to maturity, and a required return of 5%. This problem explores the concepts of present value, bond pricing, and the time value of money, ideal for finance students.

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