Question

On July 10, 2022. you purchase a $10,000 T-note that matures on December 31, 2028 (settlement occurs one day after purchase, so you receive actual ownership of the bond on July 11, 2022). The coupon rate on the Tnote is 2.125 percent and the current price quoted on the bond is 98.250 percent. The last coupon payment occurred on June 30, 2022 (11 days before settlement), and the next coupon payment will be paid on December 31, 2022 (173 days from settlement). (LG 6-2)

a. Calculate the accrued interest due to the seller from the buyer at settlement.
b. Calculate the dirty price of this transaction.

Answer 1

The accrued interest for the T-note is calculated to be approximately $12.90 by considering the principle amount, annual coupon rate, number of days in the coupon period, and the number of days from the last payment to settlement. The dirty price of the T-note is the sum of the quoted price and the accrued interest, which is $9,837.90.

Step-by-step explanation:

To calculate the accrued interest due to the seller from the buyer at settlement for the T-note, we use the formula:

Accrued Interest = Principal × (Annual Coupon Rate) × (÷ Days in Coupon Period) × (Days from Last Payment to Settlement)

At the given 2.125% coupon rate for a $10,000 T-note, and considering there are 182 days in the coupon period (as T-notes pay semi-annually and 2022 is not a leap year):

Accrued Interest = $10,000 × (0.02125) × (÷ 182) × (11)

After calculating, the total accrued interest is:

$10,000 × 0.02125 × 0.06043956 × 11 = $12.90162518

To calculate the dirty price of the transaction, add the accrued interest to the quoted price:

Dirty Price = Quoted Price + Accrued Interest

The quoted price of 98.250% of the $10,000 T-note results in $9,825. Accrued interest is approximately $12.90, so:

Dirty Price = $9,825 + $12.90 = $9,837.90

The dirty price of the T-note is $9,837.90.