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.
I believe 'at the end' is correct, as you are describing a specific point in time.
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
Here, the listener would essentially hear the sentence
On the other hand, in the end is used to refer to a more abstract notion. I could say
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
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.
In this case at the end is the only proper answer.
'at the end' means you'll do something literally near the end of something
'in the end' is more like 'after all'