When you have a payment period for the p-events, you can hide the period when the date is expired.
For example: when you have an early and late fee, you can hide the early fee when the date is expired.
To show the events which falls in the current time click on: Module content -> Registration Types -> Cog icon -> General settings
In the picture above you will find the option: Only show Registration Types In Current Period.
Click on the checkbox and save the settings.