This may seem like a dumb question, but I recently moved into my apartment on June 4th, the date on which my lease agreement began. I was asked to pay first, last and security before entering the apartment. Now, it is July 2nd and I am wondering if I owe rent this month, for my first month (as I am thinking) was paid in advance. My next payment I am thinking would be for the month of July, on August 1rst. Am I correct?

Nope. Sorry. Rent is paid in advance, which means that you pay on the first of the month for the upcoming month. When you moved in you paid June rent. Now July rent is due.

As Lisa said, yes, your first month WAS paid in advance, that was the month of June. You now owe for July.

Thank you both, it was a little confusing at first.