At the end and In the end

At the end (of something) = at the time when something ends. For example:

At the end of the month
At the end of the movie

At the end of August
At the end of the course

At the end of the match
At the end of the concert

I’m going away at the end of March/at the end of the month.
At the end of the concert, there was applause.
All the players shook hands at the end of the match.

You cannot say ‘in the end of something’. So, you cannot say ‘in the end of January’ or ‘in the end of the concert.’

*The opposite of at the end is at the beginning.

at the beginning of January – at the beginning of the concert

Children are still at the beginning of their lives.

At the beginning of the last century, thousands of people left Sweden in search of a new life.

*In the beginning means “at first,” and it usually suggests a contrast with a later situation. It is not usually followed by of.

In the beginning, computers were only used for the organization of information.

In the beginning, human beings hunted to live.

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. In the end, we sold it and bought another one (=we finally sold it)
Jim couldn’t decide where to go for his holidays. He didn’t go anywhere in the end.

The opposite of in the end is usually at first.
At first, we didn’t like each other very much, but in the end, we became good friends.

Insert at the end or in the end:

1- I normally get paid ___________of the month.

2- We had a lot of problems with our house. ___________ we sold it.
3- All the players shook hands ______________ of the match.
4- I tried to learn how to play tennis. I gave it a try quite a few times. ________________, I just gave up.
5- The students had a party for their graduation____________of the year.

Now check your answers:
1- at the end
2- in the end
3- at the end
4- in the end
5-at the end

Source: English Grammar in Use and Macmillan online dictionary