value of a forward contract after initiation

I don’t think I’m interpreting the “including accrued interest” part of the Q correctly in the following, can someone pls clarify why we need to subtract the PV of the coupon? doesn’t the price already include the coupon if it is “including accrued interest”?

270day forward on a 10Y T-bond 5% coupon which will make coupon payments in 182days and 365days. Currently selling for 98.25, risk free rate 4%. No arbitrage price for the forward contract is 98.62.

If the T-bond price decreases to 98.11 (including accrued interest) over the next 60days, the value of the short position in the 270day forward on a $10m bond is closest to:

i) $76,500

ii) $76,800

iii) $78,000


PV coupon is now 2.50/(1.04)^(122/365) = 2.467 and value of forward to long is 98.11 - 2.467 - 98.62/(1.04)^(210/365) = -0.77693 per $100 or -$77,693. So value to short ia +77,693

Accrued interest should be understood as amortization of discount or premium. Think of a discount bond. Total effective interest should be coupon +/- amortization of discount