Student in Stockholm

[92313]

I am an Australian student currently on a university exchange program in Stockholm and I am having some trouble understanding the rules regarding how long I may stay in Sweden.

I would like to remain in Sweden for a short while after my residency permit (Swedish only, not Schengen) expires on the 15th January, 2012.

Here is my situation:

I first arrived in Sweden on the 5th July 2011. I stayed for 5 days, then left but stayed in Europe until the 1st of August, where I returned to Sweden.
My residency permit began on the 24th of August.

So technically, I have only spent 30 days in Sweden without a permit.
Does this mean that I will have a remaining 60 days to stay in Sweden after my residency permit expires?
Or is this somehow affected by the fact that when my residency permit expires, it has been more than 180 days since I first entered the country?

If anyone could help me it would be greatly appreciated.

Thanks!