Which is correct?
I am planning to buy some property at the end of 2011.
I am planning to buy some property in the end of 2011.
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There is not really a grammatical rule that governs this as far as I know. It's really more a question of idiomatic usage.
One would use at the end when a specific period of time or an event is being referred to. It will almost always be followed by of and in the cases when it isn't, the of will be implicit. For example if we were at a concert, I could say
I hope they play Possum at the end.
Here, the listener would essentially hear the sentence
I hope they play Possum at the end of the show.
On the other hand, in the end is used to refer to a more abstract notion. I could say
In the end, it doesn't really matter if they finish with something else instead.
In this usage, in the end doesn't add any significant meaning to the sentence. It is serving as a qualifier though. It's presence indicates that I might be slightly disappointed if I didn't get to see Possum but in the end I'll be happy either way.
Another example would be
In the end, I'd be happy to see Harry Hood, Antelope or Divided Sky.
Here, I'm saying that as long as they play any of the songs mentioned, I'll be happy regardless of what they finish with.
So in the end is often used to say that something will change as time moves on and will eventually settle in some certain state.