The cost is really mostly for range and safety features.
Electric bikes are road legal and cheap, but not that safe. On a private trail without cars you can use two cheap options.
You can get an electric golf cart new for as low as 4k, with 5-10k being the average.
At the ultra low end you can buy an electric gokart for under 1k. Which is not that safe, sit's one person, and requires you to get really low to the ground.
PS: I think an unexplored option for a gated community is to include a custom track for electric cars to a community pool, restaurants, metro stop, etc. You would need tunnels / bridges to get around the car issue, but I think it would be cheaper than most Personal Rapid transit approaches.