A bond that matures in 9 years has a ​$1 comma 000 par value.  The annual coupon interest rate is 13 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 14 percent.  What would be the value of this bond if it paid interest​ annually?  What would be the value of this bond if it paid interest​ semiannually?  The value of this bond if it paid interest annually would be ​$
  
enter your response here.  ​(Round to the nearest​ cent.)

To calculate the value of the bond, we use the **present value formula** for bonds, which accounts for both the present value of the coupon payments and the present value of the face value at maturity.

### Formula for a bond paying interest annually:
\[
P = \sum \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}
\]
Where:
- $ P $ is the price of the bond (what we need to find).
- $ C $ is the annual coupon payment = 13% of $ 1000 $ = $ 0.13 \times 1000 = 130 $.
- $ r $ is the market’s required yield per period (14% annually or 0.14).
- $ t $ is each period (1 through 9 for annual).
- $ F $ is the face value of the bond = $ 1000 $.
- $ n $ is the number of periods = $ 9 $ years.

Let’s calculate the bond’s value.

### For annual payments:

1. The coupon payment $ C $ is \$130.
2. The yield to maturity $ r $ is 14% or 0.14.
3. The face value $ F $ is \$1000, and the bond matures in 9 years.

We’ll calculate the present value of the coupon payments and the present value of the face value, then sum them.

Now, let's calculate the bond's value.The value of the bond if it pays interest annually is approximately **$950.54**.

Now, let’s calculate the bond's value if it paid interest **semiannually**. 

For semiannual payments:
- The coupon payment is divided in half because payments are made twice per year.
- The yield per period is halved (since there are two periods per year).
- The number of periods doubles (because payments are made twice a year).

We will recalculate with these adjustments.The value of the bond if it pays interest semiannually is approximately **$949.70**.

Would you like further details on these calculations or any related concepts?

Here are 5 questions related to bond valuation:
1. How does changing the market’s required yield affect bond prices?
2. What happens to bond prices as the maturity date approaches?
3. How do you calculate the yield to maturity (YTM) for a bond?
4. How does interest rate risk affect long-term bonds compared to short-term bonds?
5. What is the difference between coupon rate and current yield?

**Tip:** Bonds with longer maturities are more sensitive to interest rate changes, meaning their prices can fluctuate more compared to shorter-term bonds.

A bond that matures in 9 years has a $1,000 par value. The annual coupon interest rate is 13 percent, and the market's required yield to maturity on a comparable-risk bond is 14 percent. What would be the value of this bond if it paid interest annually? What would be the value of this bond if it paid interest semiannually?

Calculate the value of a 9-year bond with a $1,000 par value, 13% coupon interest rate, and 14% market yield. Learn how to find the bond's value when interest is paid annually and semiannually using the present value formula. Suitable for finance students.

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