It isn't fake, NASA has all the schematics of the rocket and they are working machines. They cost way too much to design for a fake moon landing also training those astronaut takes a lot of time too.

It would be cheaper to just go to the moon rather than faking it.

The motive to go to the moon was very clear, the US wanna get ahead of the Soviet and Soviet was leading in the space race by quite a margin until the moon landing. If it was fake, the Soviet would have hammered in on the news and find every bit of infos to prove it's fake.