Question

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. b. Calculate the dirty price of this transaction.

Answer 1

a. The accrued interest due to the seller from the buyer at settlement is $171.2.

b. The dirty price of this transaction is $10,696.2.

a.  Accrued interest due to the seller from the buyer:

First step is to calculate the Accrued interest percentage using this formula

Accrued interest percentage= (Coupon rate / 2) × [Number of days before settlement / (Number of days before settlement + Number of days after settlement)]

Let plug in the formula

Accrued interest percentage=(4.375%/2)×[144/(144+40)]

Accrued interest percentage=2.1875×0.78261

Accrued interest percentage=1.712%

Second step is to calculate Accrued interest amount using this formula

 Accrued interest amount = Accrued interest % ×Face value

Let plug in the formula

 Accrued interest amount = 1.712%×$10,000

 Accrued interest amount =$171.2

b. Dirty price of this transaction:

First step is to calculate the Dirty price percentage using this formula

Dirty price percentage=Current price % + Accrued interest %

Let plug in the formula

Dirty price percentage=105.250%+1.712%

Dirty price percentage=106.962%

Second step is to calculate the Dirty price amount using this formula

Dirty price amount =Dirty price % × Face value

Let plug in the formula

Dirty price amount =106.962%×$10,000

Dirty price amount =$10,696.2

Inconclusion:

a. The accrued interest due to the seller from the buyer at settlement is $171.2.

b. The dirty price of this transaction is $10,696.2.

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