Question

A 3-yr T-note with a face value of $1000 and a coupon rate of 5.98% p.a. is trading at par. The amount of each coupon from this note is 29.9. If you hold the above T-note for 2 months and then sell it at a yield of 5% p.a., the dirty price is:

Answer 1

Face Value = $1000
Coupon rate =5.98% p.a.
Coupon = $29.9 which is paid semiannually
Holding period of T-note = 2 months
Dirty Price = Price paid for the bond (Clean Price) + Accrued Interest

Since yield is 5% p.a i.e. 2.5% semiannually, the clean price becomes
Clean Price = (29.90/1.025)+(29.9/(1.025^2))+(29.9/(1.025^3))+(29.9/(1.025^4))+(29.9/(1.025^5))+(1029.9/1.025^6)
                  = 1026.989
Accrued Interest for 61 days (30+31) = 59.8 x (61/365)
                                                      = 9.99
Thus Dirty Price = 1026.989 + 9.993
        Dirty Price = $1036.982