Question about the forward price of t bonds

Question about the pricing of t bonds. To calculate the forward contract price, it simply use the current value minus all the pv of interest , then cal the future value of it. But is the last interest in not included ? I have done few questions on it, and they didn’t included the last interest payment of t bonds, why is it?

Was the forward expiring before the bond matured?

Seems not yet expired. I will find the question out and post it here.thank you!!