Price on a bond forward contract

CFA Level II Derivatives
#1

For this question, why are they not adding and subtracting the accrued interest? I thought you would add the AI to the spot price of the bond for the 32 days prior to t=0 and subtract the AI for the 50 days after the interest payment prior to T=200. What am I missing?

Question:
Calculate the price of a 200-day forward contract on an 8%, semi-annual, U.S. Treasury bond with a spot price of $1,310. Next coupon payment will be made in 150 days. The annual risk-free rate is 5%.

The explanation with answer is:
Coupon = (1,000 × 0.08) / 2 = $40.00

Present value of coupon payment = $40.00 / 1.05^(150/365) = $39.21

Forward price on the fixed income security = ($1,310 - $39.21) × (1.05)^200/365 = $1,305.22

#2

In my opinion,spot price of $1,310 is full price at initial,which includes the interest for 32 days and it is the same reason for the treatment of interest payment prior to T=200.