Before the fiduciary monetary system (paper money system), money was made of gold or silver, which are precious metals. Therefore, any amount of increase added on the principal was obviously interest. However, purchasing power is the criterion in the current paper money system. In order to comply with the expression “neither you do wrong, nor you are wronged (al-Baqarah 2:279)”, the purchasing power of the loaned/owed money or rent must be fixed. The loss of purchasing power may be calculated by considering the inflation rate.
In your case, a fee that serves to compensate for the purchasing power loss that is caused by the late rent is NOT included in the scope of interest. Any amount more than that is counted as interest, and it must be avoided.