A company has bonds with 10-year maturity, 6.25% coupon rate with semi-annual payments, and par value of $1,000.  The market interest rate is 7.75%. What is the bond’s price?

To calculate the bond's price, we can use the **Present Value (PV)** formula for bonds, which includes the present value of the bond's coupon payments and the present value of its face value at maturity.

The bond price formula is:

\[
\text{Bond Price} = \left( \sum \frac{C}{(1 + r)^t} \right) + \frac{F}{(1 + r)^T}
\]

Where:
- $ C $ = semi-annual coupon payment = $ \frac{\text{Coupon Rate} \times \text{Par Value}}{2} $
- $ r $ = semi-annual market interest rate = $ \frac{\text{Annual Market Interest Rate}}{2} $
- $ t $ = the number of periods (for each coupon payment)
- $ F $ = face value of the bond (par value)
- $ T $ = total number of periods (maturity in semi-annual periods)

### Step-by-Step Solution:

1. **Coupon Payment**:
   - Annual coupon rate = 6.25%
   - Coupon payment = $ \frac{6.25\% \times 1,000}{2} = 31.25 $ (semi-annual).

2. **Market Interest Rate**:
   - Annual market interest rate = 7.75%
   - Semi-annual market interest rate = $ \frac{7.75\%}{2} = 3.875\% $.

3. **Number of Periods**:
   - Maturity is 10 years, with semi-annual payments, so there are $ 10 \times 2 = 20 $ periods.

4. **Face Value**:
   - Par value = $1,000.

Now, let's plug these values into the bond price formula.

\[
\text{Bond Price} = \left( \sum \frac{31.25}{(1 + 0.03875)^t} \right) + \frac{1000}{(1 + 0.03875)^{20}}
\]

I'll calculate this now.The price of the bond is approximately **$896.93**.

Would you like further details or have any questions? Here are five related questions to expand on this concept:

1. How would the bond price change if the market interest rate increased to 8.5%?
2. What happens to the bond price as the bond nears its maturity date?
3. How is the bond yield to maturity (YTM) calculated, and how does it relate to the bond price?
4. How does the bond's price change if it has annual payments instead of semi-annual?
5. What is the difference between a bond's coupon rate and the current yield?

**Tip:** As market interest rates rise, bond prices fall, and vice versa. This inverse relationship helps investors assess interest rate risk.

A company has bonds with 10-year maturity, 6.25% coupon rate with semi-annual payments, and par value of $1,000. The market interest rate is 7.75%. What is the bond’s price?

Learn how to calculate the price of a bond with a 10-year maturity, 6.25% coupon rate, and semi-annual payments. This problem involves key finance concepts like Present Value and Discounting Cash Flows. The bond's par value is $1,000, and the market interest rate is 7.75%.

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