Calculate the value of a bond that matures in 16 years and has a $ 1 comma 000 par value.  The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 13 percent. The value of the bond is ​$
  
enter your response here. ​ (Round to the nearest​ cent.)

To calculate the value of a bond, we can use the **present value formula** for bonds. The value of a bond is the sum of:

1. The present value of the coupon payments.
2. The present value of the par value at maturity.

### Given Data:
- Par value ($F$): \$1,000
- Coupon rate ($C$): 9% of \$1,000 = \$90 per year
- Yield to maturity ($r$): 13% or 0.13
- Time to maturity ($t$): 16 years

### Steps:
1. **Calculate the present value of the coupon payments:**
   - The coupon payments are an annuity, so we use the present value of an annuity formula:
   \[
   PV_{\text{coupons}} = C \times \left(1 - \frac{1}{(1 + r)^t}\right) \div r
   \]
   
2. **Calculate the present value of the par value:**
   - The par value is a lump sum payment, so we use the present value of a single sum formula:
   \[
   PV_{\text{par value}} = F \div (1 + r)^t
   \]

Now let me calculate these values for you.The value of the bond is approximately **\$735.84**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How does a change in the market interest rate affect the bond's value?
2. What happens to the bond price if the coupon rate matches the yield to maturity?
3. How is the yield to maturity (YTM) different from the coupon rate?
4. What is the relationship between bond prices and interest rate risk?
5. How would semi-annual coupon payments affect the bond value?

**Tip:** A bond’s price moves inversely to changes in the market interest rate. When rates rise, bond prices fall, and vice versa.

Calculate the value of a bond that matures in 16 years and has a $1,000 par value. The annual coupon interest rate is 9 percent and the market's required yield to maturity on a comparable-risk bond is 13 percent. The value of the bond is (Round to the nearest cent).

Discover how to calculate the value of a bond with a $1,000 par value, a 9% annual coupon rate, and a yield to maturity of 13%. Learn key concepts like present value, bond valuation, and annuity calculations with step-by-step instructions.

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