Which sounds more correct?
I am going to the post office in 2 hours
I will be going to the post office in 2 hours
Is there any difference between the two sentences?
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You can use either one, but the two have (very) slightly different emphases. "I will be going" places the emphasis on the future, but gives a hazy, not-quite-here yet, and could be altered impression. Something might prevent you, after all. However "I am going" is much stronger and places the emphasis on commitment. "I am going" means that nothing will stop you from going.
If you're asking which is correct, they both are. In this particular usage there is not much to choose between the two.
However, when we're talking about the future, the present continuous is usually used with arrangements you have already made. The continuous form with will is more of a prediction or factual assertion about what will be happening at a certain point in the future. The issue is a bit more complicated in your example, because you are using GO as the main verb. People tend to use the present continuous and the so-called going to future interchangeably when the main lexical verb is GO.
However, just to bring out the difference between the present continuous and the continuous form with will, we can show that the present continuous seems to be infelicitous (wrong) for situations that you have not already arranged, but that the so-called future continuous is fine for talking about such future events:
The first sounds wrong unless actually really have plans to do so!