At the end (of something) = at the time when something ends.
- at the end of the month
- at the end of January
- at the end of the game
- at the end of the film
- at the end of the course
- at the end of the concert
- I’m going away at the end of January / at the end of the month.
- At the end of the concert, there was great applause.
- The players shook hands at the end of the game.
You cannot say ‘in the end of …’. So you cannot say ‘in the end of January’ or ‘in the end of the concert’.
The opposite of at the end (of …) is at the beginning (of …):
- I’m going away at the beginning of January, (not in the beginning)
In the end = finally.
We use in the end when we say what the final result of a situation was:
- We had a lot of problems with our car. We sold it in the end. (= finally we sold it)
- He got more and more angry. In the end he just walked out of the room.
- Alan couldn’t decide where to go for his holidays. He didn’t go anywhere in the end. (not at the end)
The opposite of in the end is usually at first:
- At first we didn’t get on very well, but in the end we became good friends.