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The correct idiomatic expression is:

In the end:

  • Eventually; ultimately: All will turn out well in the end.

(AHD)

Compare:

In the end:

  • In the end is used mostly as an idiom that means "finally," "after a long time," or, "when everything is considered.*" It is often followed by a comma. Here are some sentences with this idiom:

Here are some sentences with this idiom:

  • We worked hard, and in the end, we achieved our goal. In the end, what really matters in a friendship is trust.

At the end:

  • At the end is used in the idiom "at the end of the day." which means something similar to in the end (= when everything is considered)
  • However, at the end is most commonly used more literally, as a prepositional phrase followed by of, to refer to the end of a specific noun. This noun can be a physical object, a period of time, an event, a place, or something more abstract, such as one's patience.

Here are some sentences with at the end + of:

  • At the end of his life, he had no regrets. Put a period at the end of every sentence. I pay the phone bill at the end of each month. There is a brick building at the end of the driveway.

(M-W)

The correct expression is:

In the end:

  • Eventually; ultimately: All will turn out well in the end.

(AHD)

Compare:

In the end:

  • In the end is used mostly as an idiom that means "finally," "after a long time," or, "when everything is considered.*" It is often followed by a comma. Here are some sentences with this idiom:
  • We worked hard, and in the end, we achieved our goal. In the end, what really matters in a friendship is trust.

At the end:

  • At the end is used in the idiom "at the end of the day." which means something similar to in the end (= when everything is considered)
  • However, at the end is most commonly used more literally, as a prepositional phrase followed by of, to refer to the end of a specific noun. This noun can be a physical object, a period of time, an event, a place, or something more abstract, such as one's patience.

Here are some sentences with at the end + of:

  • At the end of his life, he had no regrets. Put a period at the end of every sentence. I pay the phone bill at the end of each month. There is a brick building at the end of the driveway.

(M-W)

The correct idiomatic expression is:

In the end:

  • Eventually; ultimately: All will turn out well in the end.

(AHD)

Compare:

In the end:

  • In the end is used mostly as an idiom that means "finally," "after a long time," or, "when everything is considered.*" It is often followed by a comma.

Here are some sentences with this idiom:

  • We worked hard, and in the end, we achieved our goal. In the end, what really matters in a friendship is trust.

At the end:

  • At the end is used in the idiom "at the end of the day." which means something similar to in the end (= when everything is considered)
  • However, at the end is most commonly used more literally, as a prepositional phrase followed by of, to refer to the end of a specific noun. This noun can be a physical object, a period of time, an event, a place, or something more abstract, such as one's patience.

Here are some sentences with at the end + of:

  • At the end of his life, he had no regrets. Put a period at the end of every sentence. I pay the phone bill at the end of each month. There is a brick building at the end of the driveway.

(M-W)

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source | link

The correct expression is:

In the end:

  • Eventually; ultimately: All will turn out well in the end.

(AHD)

Compare:

In the end:

  • In the end is used mostly as an idiom that means "finally," "after a long time," or, "when everything is considered.*" It is often followed by a comma. Here are some sentences with this idiom:
  • We worked hard, and in the end, we achieved our goal. In the end, what really matters in a friendship is trust.

At the end:

  • At the end is used in the idiom "at the end of the day." which means something similar to in the end (= when everything is considered)
  • However, at the end is most commonly used more literally, as a prepositional phrase followed by of, to refer to the end of a specific noun. This noun can be a physical object, a period of time, an event, a place, or something more abstract, such as one's patience.

Here are some sentences with at the end + of:

  • At the end of his life, he had no regrets. Put a period at the end of every sentence. I pay the phone bill at the end of each month. There is a brick building at the end of the driveway.

(M-W)