Question 1173160: A 1000$,5% bond with annual coupons will be redeemed at the end of 9 years. Find the price to yield (a) 4%
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Okay, let's calculate the bond price for this scenario.
**Understanding the Bond**
* **Face Value:** $1,000
* **Coupon Rate:** 5% per year (paid annually)
* **Yield to Maturity (YTM):** 4% per year
* **Redemption at Par:** The bond will be redeemed for its face value ($1,000) at maturity.
* **Time to Maturity:** 9 years
**Calculations**
1. **Annual Coupon Payment:**
* Annual coupon payment: $1,000 \* 0.05 = $50
2. **Annual Yield Rate:**
* Annual yield rate: 4% or 0.04
3. **Number of Periods:**
* 9 years (annual payments)
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 4%**
* Bond Price = ($50 \* [1 - (1 + 0.04)^-9] / 0.04) + ($1,000 / (1 + 0.04)^9)
* Bond Price = ($50 \* [1 - (1.04)^-9] / 0.04) + ($1,000 / (1.04)^9)
* Bond Price = ($50 \* [1 - 0.702586] / 0.04) + ($1,000 / 1.423311)
* Bond Price = ($50 \* [0.297414] / 0.04) + (702.586)
* Bond Price = ($50 \* 7.43535) + 702.586
* Bond Price = 371.7675 + 702.586
* Bond Price = $1074.35 (approximately)
**Result**
* (a) The price of the bond to yield 4% is approximately $1,074.35.
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