Question

On October 5, 2019, you purchase a $10,000 T-note that matures on August 15, 2031 (settlement occurs one day after purchase, so you receive actual ownership of the bond on October 6, 2019). The coupon rate on the T-note is 4.375 percent and the current price quoted on the bond is 105.250 percent. The last coupon occurred on May 15, 2019 (144 days before settlement), and the next coupon payment will be paid on November, 2019 (40 days from settlement).

a) Calculate the accrued interest (per face value of the bond) due to the seller from the buyer at settlement.

b) Calculate the dirty price (per face value of the bond) of this transaction . Leave your final answer in 3 decimal places.

Answer 1

A) $171.196

B) $10,696.196

Step-by-step explanation:

A) accrued interest owed to the seller:

$10,000 x 4.375% x 1/2 (semiannual coupon) x 144/184 days = $171.196* ≈ $171.20

B) the dirty price of the bond includes accrued interest earned by the bond + the bond's market price

• accrued interest = $171.196
• bond's market price = $10,000 x 105.25% = $10,525

bond's dirty price = $171.196 + $10,525 = $10,696.196*

*Answer includes 3 decimal places.

Answer 2

a)

Accrued interest percentage is 1.712%

Accrued interest amount is $171.2

b)

Dirty price percentage is 106.962%

Dirty price amount is $10696.2

Step-by-step explanation:

Given:

coupon rate = 4.375% = 0.04375

number of days before settlement = 144 days

number of days after settlement = 40 days

Face value = $10000

current price % = 105.250%

a)

Accrued interest percentage = (coupon rate / 2) × [number of days before settlement / (number of days before settlement + number of days after settlement)] = (0.04375/2) × 144 / (144 + 40) = 0.01712 = 1.712%

Accrued interest percentage is 1.712%

Accrued interest amount = accrued interest × face value = 0.01712 × 10000 = $171.2

Accrued interest amount is $171.2

b)

Dirty price percentage = current price % + accrued interest % = 105.25 + 1.712 = 106.962% = 1.06962

Dirty price percentage is 106.962%

Dirty price amount = dirty price % × face value = 1.06962 × 10000 = $10696.2

Dirty price amount is $10696.2