Count unique values on a specific date

I figured out a way to count the unique customers. But the problem I am now facing is to count the relevant customers. I need to count only the active customers on 31st of each year. Since they all have different periods it makes it difficult. For example: Customer 2 is active on
22.February 2013 and since it doesīt have an inactive date it is thus active on 31st of December 2013. Customer 3, however, is active 22nd of
February 2013, but inactive 1st of December 2013, so therefor I canīt count customer 3 in 2013. I have attached a new file.

Hopefully somebody understands my challenge.