Question 1208648: Union Local School District has a bond outstanding with a coupon rate of 3.2 percent paid semiannually and 21 years to maturity. The yield to maturity on this bond is 3.5 percent, and the bond has a par value of $5,000. What is the dollar price of the bond?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the bond price:
**1. Determine the variables:**
* **Par Value (FV):** $5,000
* **Coupon Rate:** 3.2% per year (paid semiannually)
* **Yield to Maturity (YTM):** 3.5% per year (compounded semiannually)
* **Time to Maturity:** 21 years
**2. Calculate the semiannual coupon payment:**
* Semiannual Coupon Payment = (Coupon Rate / 2) * Par Value
* Semiannual Coupon Payment = (0.032 / 2) * $5,000
* Semiannual Coupon Payment = $80
**3. Calculate the number of periods (n):**
* n = Time to Maturity (in years) * 2 (semiannual periods)
* n = 21 * 2
* n = 42
**4. Calculate the semiannual yield to maturity (r):**
* r = YTM / 2
* r = 0.035 / 2
* r = 0.0175
**5. Use the present value formula for a bond:**
Bond Price = (C * [1 - (1 + r)^-n] / r) + (FV / (1 + r)^n)
Where:
* C = Semiannual coupon payment
* r = Semiannual yield to maturity
* n = Number of periods
* FV = Par value
Bond Price = ($80 * [1 - (1 + 0.0175)^-42] / 0.0175) + ($5,000 / (1 + 0.0175)^42)
Bond Price = ($80 * [1 - 0.5021] / 0.0175) + ($5,000 / 2.0084)
Bond Price = ($80 * 0.4979 / 0.0175) + $2489.51
Bond Price = $2276.23 + $2489.51
Bond Price = $4765.74
Therefore, the dollar price of the bond is approximately $4765.74.
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