Borrowed long position money and shorting

I am a bit confused on paying interest on long positions that borrowed money when it also comes to shorting other stocks at the same time.

For example:
Say I invest 10K cash, so the buying power is 20K.

I buy 12K worth of shares from stock XYZ. So my cash is shown to be -2K ie currently borrowing 2K. From this I can calculate my daily margin interest costs given that I can see 2K has been borrowed. But say I short a stock for 6K worth of shares. Now my cash is shown to be -2K + 6K = 4K.

Does this mean I would no longer be paying a margin interest on that long position? And if I still am paying interest how am I suppose to know exactly how much is being borrowed for this long position since my cash is no longer negative?