Question 1173161: A 1000$, 4.5% bond with semi annual coupons will be redeemed at the end of 15 years. Find the price to yield (a) 3%
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's calculate the price of the bond step-by-step:
**Understanding the Bond**
* **Face Value:** $1,000
* **Coupon Rate:** 4.5% per year (paid semi-annually)
* **Yield to Maturity (YTM):** 3% per year (semi-annual yield)
* **Redemption at Par:** The bond will be redeemed for its face value ($1,000) at maturity.
* **Time to Maturity:** 15 years
**Calculations**
1. **Semi-annual Coupon Payment:**
* Annual coupon payment: $1,000 \* 0.045 = $45
* Semi-annual coupon payment: $45 / 2 = $22.50
2. **Semi-annual Yield Rate:**
* Annual yield rate: 3% or 0.03
* Semi-annual yield rate: 0.03 / 2 = 0.015
3. **Number of Periods:**
* 15 years \* 2 periods/year = 30 periods
4. **Bond Pricing Formula:**
* Bond Price = (Coupon Payment \* [1 - (1 + Yield Rate)^-Periods]) / Yield Rate + (Face Value / (1 + Yield Rate)^Periods)
**Applying the Formula**
**(a) Yield to Maturity of 3%**
* Bond Price = ($22.50 \* [1 - (1 + 0.015)^-30] / 0.015) + ($1,000 / (1 + 0.015)^30)
* Bond Price = ($22.50 \* [1 - (1.015)^-30] / 0.015) + ($1,000 / (1.015)^30)
* Bond Price = ($22.50 \* [1 - 0.638659] / 0.015) + ($1,000 / 1.55816)
* Bond Price = ($22.50 \* [0.361341] / 0.015) + (641.78)
* Bond Price = ($22.50 \* 24.0894) + 641.78
* Bond Price = 542.0115 + 641.78
* Bond Price = $1183.79 (approximately)
**Result**
* (a) The price of the bond to yield 3% is approximately $1,183.79.
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