Aggregate based on values in two tables

I have been struggling with what I feel should be a fairly simple problem and am going around in circles at this point. I have some data relating to application processing times. The main table contains application start and completion dates, and I am trying to get a count of the number of applications which are active (ie. started but not yet completed) at the end of a given quarter. Missing end dates indicated that the application is not yet complete. I have an aggregated table which contains quarter end dates and some other data which has been aggregated from the main table. I want to add the count of active applications for each quarter end date to this table. See sample data below. Help would be appreciated!

Quarter end dates (in aggregated table)Application start and end dates (in main table)