Hi,
Check this post and Yadav's comment-
How to use 'at selection screen on exit command'
So what you need to do is not to mark the billing period field as obligatory but still you get the tick in the field which looks like mandatory.
In the PAI (At selection-screen event) you can check if the user checked the other radio button in which case just show the other screen. If the user presses enter or execute, display the error message and dont let him navigate to output.
Best regards,
Saurabh