SOLUTION: A 10,000$, 5% with semi annual coupons is price to yield 7%. Find the price if the bond is redeemable at par at the end of (a) 10years, (b) 15years

Question 1173162: A 10,000$, 5% with semi annual coupons is price to yield 7%. Find the price if the bond is redeemable at par at the end of (a) 10years, (b) 15years
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's break down how to calculate the price of a bond with semi-annual coupons.
**Understanding the Bond**
* **Face Value:** $10,000
* **Coupon Rate:** 5% per year (paid semi-annually)
* **Yield to Maturity (YTM):** 7% per year (semi-annual yield)
* **Redemption at Par:** The bond will be redeemed for its face value ($10,000) at maturity.
**Calculations**
1. **Semi-annual Coupon Payment:**
* Annual coupon payment: $10,000 \* 0.05 = $500
* Semi-annual coupon payment: $500 / 2 = $250
2. **Semi-annual Yield Rate:**
* Annual yield rate: 7% or 0.07
* Semi-annual yield rate: 0.07 / 2 = 0.035
3. **Number of Periods:**
* (a) 10 years: 10 years \* 2 periods/year = 20 periods
* (b) 15 years: 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) 10 Years (20 Periods)**
* Bond Price = ($250 \* [1 - (1 + 0.035)^-20] / 0.035) + ($10,000 / (1 + 0.035)^20)
* Bond Price = ($250 \* [1 - 0.5025656] / 0.035) + ($10,000 / 1.98978886)
* Bond Price = ($250 \* 14.212411) + (5025.656)
* Bond Price = $3553.10275 + $5025.656
* Bond Price = $8578.76 (approximately)
**(b) 15 Years (30 Periods)**
* Bond Price = ($250 \* [1 - (1 + 0.035)^-30] / 0.035) + ($10,000 / (1 + 0.035)^30)
* Bond Price = ($250 \* [1 - 0.356276] / 0.035) + ($10,000 / 2.80678)
* Bond Price = ($250 \* 18.392114) + (3562.76)
* Bond Price = 4598.0285 + 3562.76
* Bond Price = $8160.79 (approximately)
**Results**
* (a) The price of the bond with 10 years to maturity is approximately $8,578.76.
* (b) The price of the bond with 15 years to maturity is approximately $8,160.79.

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