USAA Charged for terminated credit card San Antonio Texas

I terminated my American Express Credit Card on June 13, 2016.  I was charged 35.00 annual fee every year for the following year.  This time it was for 2016-2017.  In July I kept getting late charges which I did not pay since the card had been closed.  This was reflected on my credit report.  I called USAA and they explained that I still had to pay now $36.31 with interest even though my card had been closed.  They told me that I was billed on May 12 for 2016-2017 but I terminated in June so I have to pay the annual feel.  They apologized that they did not explain that to me when I terminated the card.  I asked since I have to pay to give me another card.  They told me I would have to apply for a new card and that would cost another $35.00 annual fee since it would be a new card.  I asked what am I getting for $36.31 for 2016-2017 thy said "nothing" just pay it.