Forward Contracts on bonds

if I am having the current price on an US T-bond let’s say it is $1,071.77. The forward contract will expire in 195 days and it carries a 6% coupon that is paid semiannual.

In order to get the contract’s price, I will subtract the present value of the coupon due.

My question is; will I subtract it from the current value of the contract which is $1,071.77 or from the par value which is $1,000, and in case I will subtract it from the current value, why is that?

You will subtract the present value of any coupons due within the next 195 days.

You subtract that present value from the spot price of the bond. That spot price is for a bond that will receive the coupon payment(s). The holder of the forward won’t receive the coupon payment(s), so she doesn’t have to pay for them.