-(으)ㄴ 끝에

Shows that a result was finally reached after a long or difficult process of doing something.

시간·순서Time & sequence

Han: 끝에 marks the end of a process that is already finished, so the verb must take the past modifier -(으)ㄴ, not the present -는.

Examples

두 사람은 몇 시간 동안 논의한 끝에 합의에 이르렀다.After discussing it for several hours, the two finally reached an agreement.

여러 번 실패한 끝에 드디어 운전면허 시험에 합격했어요.After failing several times, I finally passed the driving test.

오랜 고민 끝에 유학을 가기로 결정했습니다.After long deliberation, I decided to go abroad to study.

3년 동안 준비한 끝에 작은 카페를 열게 되었어요.After preparing for three years, I was finally able to open a small café.

-(으)ㄴ 끝에vs-(으)ㄴ 나머지나머지 means an extreme state or feeling caused an (often unwanted) result, not a long process: 너무 긴장한 나머지 실수를 했어요.

V+(으)ㄴ 끝에

N+끝에

고민하다 → 고민한 끝에, 찾다 → 찾은 끝에, 노력 → 노력 끝에

Verbs take only the past modifier -(으)ㄴ, not -는 or -(으)ㄹ; nouns attach directly (고민 끝에, 노력 끝에).
The first action is usually long or hard (often with 오랫동안, 여러 번, 고민하다, 노력하다); it sounds odd with short routine actions like eating a meal.
The main clause usually states an outcome already reached, in the past tense; it is not normally used with commands or suggestions (-(으)세요, -자).
The result is often marked with 드디어, 마침내 or 결국, and it can be positive or negative (결국 포기했다).

Wrong: ~~오랫동안 고민하는 끝에 회사를 그만두기로 했어요.~~

Right: 오랫동안 고민한 끝에 회사를 그만두기로 했어요.

끝에 marks the end of a process that is already finished, so the verb must take the past modifier -(으)ㄴ, not the present -는.

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