You purchase a bond with an invoice price of $1,021. The bond has a coupon rate of 5.48 percent, it makes semiannual payments, and there are 4 months to the next coupon payment. The par value is $1,000. What is the clean price of the bond?

Multiple Choice

$1,011.87

$993.60

$1,030.13

$1,002.73

$1,048.40

To find the clean price of the bond, we need to separate the bond's invoice price into its clean price and accrued interest.

1. **Identify Given Information**:
   - Invoice price (full price) of the bond: $1,021
   - Coupon rate: 5.48% (annual)
   - Semiannual coupon payments
   - Par value: $1,000
   - Time remaining to the next coupon: 4 months

2. **Calculate the Semiannual Coupon Payment**:
   Since the coupon rate is 5.48% annually, and payments are semiannual, each payment is:
   \[
   \text{Coupon payment} = \frac{5.48\% \times 1000}{2} = \frac{54.80}{2} = 27.40
   \]

3. **Determine Accrued Interest**:
   Accrued interest is based on the time since the last coupon payment. Since there are 4 months to the next payment and payments are semiannual (every 6 months), it has been 2 months since the last payment.

   Accrued interest formula:
   \[
   \text{Accrued interest} = \text{Coupon payment} \times \frac{\text{Months since last payment}}{\text{Total months in payment period}}
   \]
   Substituting values:
   \[
   \text{Accrued interest} = 27.40 \times \frac{2}{6} = 27.40 \times 0.3333 = 9.13
   \]

4. **Calculate the Clean Price**:
   The clean price is the invoice price minus the accrued interest.
   \[
   \text{Clean price} = 1021 - 9.13 = 1011.87
   \]

5. **Answer**:
   The clean price of the bond is **$1,011.87**.

### Final Answer:
**$1,011.87**

Would you like further details on any step or have any questions?

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Here are five related questions to deepen understanding:
1. How would the clean price change if the time since the last payment was 3 months instead of 2?
2. What is the accrued interest if the bond has a coupon rate of 6% instead?
3. How does the invoice price relate to clean and dirty prices of bonds?
4. How would the price differ if payments were annual instead of semiannual?
5. What would the accrued interest be if the bond’s par value was $5,000?

**Tip**: Always separate accrued interest from the bond's full price to understand clean vs. dirty prices in bond pricing.

You purchase a bond with an invoice price of $1,021. The bond has a coupon rate of 5.48 percent, it makes semiannual payments, and there are 4 months to the next coupon payment. The par value is $1,000. What is the clean price of the bond?

Learn how to calculate the clean price of a bond given an invoice price, a 5.48% coupon rate, semiannual payments, and 4 months to the next coupon. Detailed steps cover calculating the semiannual coupon, accrued interest, and bond clean price. Ideal for students in Grades 11-12.

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