We run CiviCRM 4.7.21. In events, we are able to indicate a registration payment toward the total with the balance owed within each participant's registration page. However, we have not been able to determine how to run a report that indicates partial payment and balance owed. Is there an event or contribution report that can be configured to run a report that shows both the partial payment amount and the balance owed?
welcome to civicrm stackexchange. I can't answer your question specifically as a quick search for a report that does this didn't turn anything up.
The wiki page for partial payments is here but i don't see anything specifically indicating new reports were created for it but rather that
Existing search and report filters allow users to filter on Participant and Membership status, and therefore can be used as-is to locate partially paid records. Reports which calculate revenue based on completed contribution summation should continue to provide accurate revenue totals.
There are a couple of additional report solutions that may be worth investigating but I suspect neither have yet accommodated the 'partial payment' issue (which I haven't seen in use personally). The two I am thinking of are