A 10-year Treasury bond with par value of $1,000 has a 6% p.a. coupon rate and pays interest every six months.  The bond is four years old and has just made its eighth payment.  The market now requires a 7% p.a. return on the bond.  What is the expected price of the bond?


Group of answer choices

$981.63

$965.63

$951.68

$809.34

$1,000.00

To calculate the price of a bond, we use the present value of future cash flows, which includes coupon payments and the bond's face value at maturity. In this case, we are dealing with semi-annual coupon payments. The formula for the bond price is:

\[
P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n}
\]

Where:
- $ P $ is the bond price
- $ C $ is the semi-annual coupon payment
- $ r $ is the semi-annual yield required by the market
- $ F $ is the face value (par value) of the bond
- $ n $ is the total number of remaining periods

### Given Information:
- **Par value ($ F $)** = $1,000
- **Annual coupon rate** = 6% → Semi-annual coupon rate = 3%
- **Coupon payment ($ C $)** = $ 1,000 \times 3\% = 30 $
- **Years remaining** = 6 years (10-year bond is 4 years old) → 12 remaining semi-annual periods
- **Market yield (annual)** = 7% → Semi-annual market yield = $ \frac{7\%}{2} = 3.5\% $

### Step-by-step Solution:

1. **Present value of coupon payments**: 
   These are the periodic $ C = 30 $ payments over the next 12 periods, discounted at $ r = 0.035 $ per period.

\[
PV_{\text{coupons}} = \sum_{t=1}^{12} \frac{30}{(1 + 0.035)^t}
\]

2. **Present value of the par value at maturity**:
   This is the face value ($1,000) discounted back for 12 periods at the semi-annual rate of 3.5%.

\[
PV_{\text{face}} = \frac{1,000}{(1 + 0.035)^{12}}
\]

Now, I'll calculate these values.

The expected price of the bond is approximately **$951.68**.

Thus, the correct answer is:

**$951.68**.

Would you like more details on how the calculations were done, or do you have any further questions?

Here are five related questions:
1. How does the bond price change if the market interest rate increases?
2. What would the bond price be if it had no coupon payments (zero-coupon bond)?
3. How does the time to maturity affect bond prices?
4. How would a different coupon rate impact the bond's price calculation?
5. What happens to the bond price when the market interest rate matches the coupon rate?

**Tip:** When interest rates rise, bond prices typically fall, and vice versa. This is due to the inverse relationship between bond prices and market interest rates.

A 10-year Treasury bond with par value of $1,000 has a 6% p.a. coupon rate and pays interest every six months. The bond is four years old and has just made its eighth payment. The market now requires a 7% p.a. return on the bond. What is the expected price of the bond?

Learn how to calculate the expected price of a 10-year Treasury bond with a par value of $1,000 and a 6% coupon rate. This problem involves finding the present value of future cash flows, given a 7% market return. Suitable for finance and investment students.

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