What is the current value of a $1,000 bond with a 6% annual coupon rate (paid semi-annually) that matures in 11 years if the appropriate stated annual discount rate is 12%

We need to calculate the current value (price) of a bond that has a par value of $1,000, an annual coupon rate of 6% (paid semi-annually), and matures in 11 years. The stated annual discount rate is 12%, which we'll also convert to a semi-annual rate for consistency.

### Steps to solve the problem:

1. **Identify the bond's key values**:
   - **Par Value (Face Value)**: $1,000
   - **Coupon Rate**: 6% annually, but since the bond pays semi-annually, each coupon payment will be 3% of the face value every six months.
   - **Maturity (Years)**: 11 years
   - **Stated Annual Discount Rate (Yield)**: 12% annually, or 6% semi-annually.

2. **Determine the semi-annual coupon payment**:
   \[
   \text{Semi-annual coupon payment} = \frac{6\%}{2} \times 1000 = 30
   \]

3. **Number of periods**:
   Since payments are made semi-annually and the bond matures in 11 years:
   \[
   \text{Number of periods} = 11 \times 2 = 22
   \]

4. **Discount rate per period**:
   The semi-annual discount rate is half of the annual discount rate:
   \[
   \text{Semi-annual discount rate} = \frac{12\%}{2} = 6\%
   \]

5. **Calculate the present value of coupon payments**:
   The coupon payments represent an annuity over 22 periods. We can use the present value of an annuity formula:
   \[
   PV_{\text{coupons}} = 30 \times \left( 1 - \frac{1}{(1 + 0.06)^{22}} \right) \div 0.06
   \]

6. **Calculate the present value of the face value**:
   The face value is paid at the end of the bond's maturity (at the end of 22 periods), and we discount it back to the present:
   \[
   PV_{\text{face}} = 1000 \times \frac{1}{(1 + 0.06)^{22}}
   \]

7. **Add the present values**:
   The bond's price is the sum of the present value of the coupon payments and the present value of the face value.

Let's calculate it step by step.# Given values
par_value = 1000  # Face value of the bond
semi_annual_coupon_rate = 0.06 / 2  # Semi-annual coupon rate (6% annual)
semi_annual_discount_rate = 0.12 / 2  # Semi-annual discount rate (12% annual)
number_of_periods = 11 * 2  # Number of periods (semi-annual, 11 years)

# Coupon payment per period
coupon_payment = par_value * semi_annual_coupon_rate

# Calculate the present value of the annuity (coupon payments)
pv_coupons = coupon_payment * (1 - (1 / (1 + semi_annual_discount_rate) ** number_of_periods)) / semi_annual_discount_rate

# Calculate the present value of the face value (lump sum at maturity)
pv_face_value = par_value / (1 + semi_annual_discount_rate) ** number_of_periods

# Total present value of the bond (price)
bond_price = pv_coupons + pv_face_value
bond_priceThe current value (price) of the $1,000 bond, with a 6% annual coupon rate (paid semi-annually) and maturing in 11 years, discounted at a 12% annual rate, is approximately **$638.75**.

Would you like more details on how each component was calculated, or do you have any other questions?

Here are 5 related questions to consider:
1. How does the bond price change if the discount rate decreases to 10%?
2. What is the relationship between bond prices and interest rates?
3. How would the bond price change if coupon payments were annual instead of semi-annual?
4. What happens to the bond price as the bond nears its maturity date?
5. How do zero-coupon bonds differ in their price calculation compared to coupon bonds?

**Tip:** Bond prices and interest rates move in opposite directions. When rates rise, bond prices fall, and vice versa.

Learn how to calculate the current value (price) of a $1,000 bond with a 6% annual coupon rate (paid semi-annually) that matures in 11 years, discounted at a 12% annual rate. Understand the present value formulas for coupon payments and face value, and their application in bond valuation.

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