On October 5, 2022, you purchase a $10,000 Treasury-note that matures on August 15, 2031 (settlement occurs one day after purchase, so you receive actual ownership of the bond on October 6, 2022). The coupon rate on the Treasury-note is 4.375 percent and the current price quoted on the bond is 105.250 percent. The last coupon payment occurred on May 15, 2022 (144 days before settlement), and the next coupon payment will be paid on November 15, 2022 (40 days from settlement).



a. Calculate the accrued interest due to the seller from the buyer at settlement. Write this in dollars based on the $10,000 face value of the Treasury-note. Round your answer to the nearest penny ($235.56)

Accrued Interest Due the Seller: $


b. Calculate the dirty price of this transaction. Write this in dollars based on the $10,000 face value of the Treasury-note. Round your answer to the nearest penny ($235.56)

Dirty Price: $



To solve these questions, let's break down each part with the necessary formulas and calculations.

### Given Data:
- **Face Value** ($ F $) = $10,000
- **Coupon Rate** ($ c $) = 4.375%
- **Quoted Price** = 105.250%
- **Last Coupon Payment** = May 15, 2022
- **Settlement Date** = October 6, 2022
- **Next Coupon Payment** = November 15, 2022
- **Days from Last Coupon to Settlement** = 144 days
- **Days in Coupon Period** (from May 15, 2022, to November 15, 2022) = $ 144 + 40 = 184 $ days

#### Coupon Payment Amount
The bond has a 4.375% annual coupon rate, paid semiannually, so the semiannual coupon payment $ C $ is:
\[
C = \frac{4.375\%}{2} \times 10,000 = 0.021875 \times 10,000 = 218.75
\]

### Part (a): Accrued Interest
Accrued interest (AI) is calculated as follows:
\[
\text{Accrued Interest} = C \times \frac{\text{Days from Last Coupon to Settlement}}{\text{Days in Coupon Period}}
\]
Substitute the known values:
\[
\text{Accrued Interest} = 218.75 \times \frac{144}{184}
\]
\[
\text{Accrued Interest} = 218.75 \times 0.7826 = 171.74
\]
Thus, the **accrued interest due to the seller** is approximately **$171.74**.

### Part (b): Dirty Price
The dirty price is the quoted (clean) price plus the accrued interest. Here’s the calculation:

#### Clean Price
The clean price is the quoted price as a percentage of the face value:
\[
\text{Clean Price} = 105.250\% \times 10,000 = 1.0525 \times 10,000 = 10,525
\]

#### Dirty Price
Now, add the accrued interest to get the dirty price:
\[
\text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest}
\]
\[
\text{Dirty Price} = 10,525 + 171.74 = 10,696.74
\]

### Final Answers:
- **(a) Accrued Interest Due to the Seller:** $171.74
- **(b) Dirty Price:** $10,696.74

Do you have questions or would you like further details on any step?

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Here are 5 related questions for further practice:

1. How would the accrued interest change if the settlement was a month earlier?
2. What is the impact on the dirty price if the coupon rate were higher?
3. How would accrued interest be calculated for a bond with quarterly coupon payments?
4. What would be the clean and dirty prices if the quoted price was 100%?
5. How does the accrued interest affect the buyer's return if they hold the bond to maturity?

**Tip:** Remember that Treasury-note prices are quoted as a percentage of the bond’s face value.

On October 5, 2022, you purchase a $10,000 Treasury-note that matures on August 15, 2031 (settlement occurs one day after purchase, so you receive actual ownership of the bond on October 6, 2022). The coupon rate on the Treasury-note is 4.375 percent and the current price quoted on the bond is 105.250 percent. The last coupon payment occurred on May 15, 2022 (144 days before settlement), and the next coupon payment will be paid on November 15, 2022 (40 days from settlement). a. Calculate the accrued interest due to the seller from the buyer at settlement. Write this in dollars based on the $10,000 face value of the Treasury-note. Round your answer to the nearest penny ($235.56) Accrued Interest Due the Seller: $ b. Calculate the dirty price of this transaction. Write this in dollars based on the $10,000 face value of the Treasury-note. Round your answer to the nearest penny ($235.56) Dirty Price: $

Learn how to calculate the accrued interest and dirty price for a Treasury-note with a 4.375% coupon rate and a quoted price of 105.250%. This bond valuation example covers key finance concepts, including interest calculation and clean vs. dirty price. Suitable for advanced high school and college-level students.

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