Put call forward parity

Forward plus risk free bond equal call plus risk free bond.

Is it correct formula ?

Why it contradicts with book ?

This is not the formula. The formula for put call parity is the following:

Stock + Put = Call + X (risk free zero coupon bond payoff)/ (1+r)t

Protective put = Fiduciary call

The forward version replaces the stock value with a forward contract:

F/(1+r)t + Put = Call + X (risk free zero coupon bond payoff)/ (1+r)t

Put = Call + (X-F)/(1+r)t

How can you replace So with Fo(T)/(1+r)t ? As per the curriculum

risk free bond + Forward = Asset

Would you please explain.

What’s the arbitrage-free forward price?

F0(T) = S0(1 + r)T

Solve for S0:

S0 = F0(T) / (1 + r)T