Question

On 10/12/2020, a U.S. Treasury bond has a face value $1,000, maturity at 8/10/2022, a coupon rate of 7.2%, semi-annual coupon payments, and yield to maturity (BEY) of 5.6%. As of 10/12/2020, there have been 63 days since the last coupon payment. There are 184 days between 8/10/2020 and 2/10/2021. What are the bond’s clean price and dirty price? Keep the final answers in 2 decimal places, e.g., $10.12.

Answer 1

Accrued Interest = F * (C/M) * (D/T)

where F = Face Value = $1,000
C = Coupon Rate = 7.2%
M = Number of coupon Payments in a year = 2 (Semi-Annual)
D = Days since last coupon payment was done = 63 days
T = Number of Days between 2 coupon payments = 184 days

Accrued Interest = 1000 * (7.2%/2) * (63/184)
= 12.32608696
Clean Price = $1,027.3224

Dirty Price = Clean Price + Accrued Interest
= 1,027.3224 + 12.32608696
Dirty Price =  $1,039.6485