Either is possible, plausible and within the scope of the theory. Personally I would prefer an orientation towards an annual (or even monthly) payment as renting "site value". Many LVT advocates (myself included) suggest that this payment should the entire unimproved site value.

In other words, whilst you would pay interest for "borrowing" a building from a home-owner, you would rent the land from the community.

With regards to rapidly inflated values these would only be likely if there were sudden development in the region; in which case holding on to the land in an uneconomic manner would retard productivity.