Yan Yan Corporation has a $3,000 par value bond outstanding with a coupon rate of 4.4 percent paid semiannually and 20 years to maturity. The yield to maturity of the bond is
5.1 percent. What is the dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Bond price

To calculate the price of a bond, we use the present value formula for the bond's future cash flows. The price of a bond is the sum of the present value of its coupon payments and the present value of its face value (par value).

### Step-by-step breakdown:

1. **Given Information:**
   - **Par value (Face value)** = $3,000
   - **Coupon rate** = 4.4% per year, paid semiannually
   - **Time to maturity** = 20 years
   - **Yield to maturity (YTM)** = 5.1% per year, compounded semiannually

2. **Coupon Payment:**
   Since coupon payments are made semiannually, we divide the annual coupon rate by 2:
   \[
   \text{Coupon payment} = 3,000 \times \left(\frac{4.4\%}{2}\right) = 3,000 \times 0.022 = 66
   \]
   Each semiannual coupon payment is $66.

3. **Number of Periods:**
   There are 20 years, and payments are made semiannually, so the total number of periods is:
   \[
   \text{Total periods} = 20 \times 2 = 40 \text{ periods}
   \]

4. **YTM per Period:**
   Since the yield to maturity is compounded semiannually, the YTM per period is:
   \[
   \text{YTM per period} = \frac{5.1\%}{2} = 2.55\% = 0.0255
   \]

5. **Present Value of Coupon Payments:**
   The present value of the coupon payments is calculated as the present value of an annuity:
   \[
   PV_{\text{coupons}} = 66 \times \left(1 - \frac{1}{(1 + 0.0255)^{40}}\right) \div 0.0255
   \]

6. **Present Value of Par Value:**
   The present value of the face value (par value) is:
   \[
   PV_{\text{par}} = 3,000 \times \frac{1}{(1 + 0.0255)^{40}}
   \]

Now let's calculate the bond price using these formulas.The price of the bond is approximately **$2,738.63**.

Would you like further details on how this was calculated, or do you have any other questions?

Here are 5 related questions you might find useful:
1. How does a bond’s price change if the yield to maturity increases?
2. What is the impact of different coupon rates on bond pricing?
3. How are zero-coupon bonds priced compared to coupon-paying bonds?
4. What is the relationship between bond prices and interest rates?
5. How does time to maturity affect the sensitivity of bond prices to interest rate changes?

**Tip:** Bonds with longer maturities are more sensitive to interest rate changes than those with shorter maturities.

Yan Yan Corporation has a $3,000 par value bond outstanding with a coupon rate of 4.4 percent paid semiannually and 20 years to maturity. The yield to maturity of the bond is 5.1 percent. What is the dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Learn how to calculate the price of a bond for Yan Yan Corporation, with a $3,000 par value, a 4.4% coupon rate, and 5.1% yield to maturity. This detailed breakdown includes the present value of coupon payments and the bond's face value using the annuity and present value formulas. Suitable for finance students.

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