Database Design - Monthly server billing tracker

I am trying to design a simple SQLite database to bill players on a server. The server is paid for on a monthly basis at a cost of $10 (but this might change). I would like to have the following tables (or something better):

Months:
-id (int primary key)
-ref (text) something like "JAN11 just for readability"
-cost (real) something like 10 or 9.5 the monthly cost of the server

Players:
-id (int primary key)
-name (text)

The cost should be divided among the players who logged on at the end of th开发者_如何学Ce month (ie. 5 people log in in January they get the $10 split among them).

In short: I don't know how to store whether or not the players logged in during the month so as to divide the cost among them.

Another good table to have would be Logins, e.g.:

Logins:
    id int,
    player_id int,
    month_id int

That way you could just check if a player logged in, or even also check how many times they logged in (assuming you wanted to track that).