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.