to accept / compensate
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to come to terms with
To reluctantly accept an unpleasant or unchangeable situation and stop resisting it.
Er musste sich damit abfinden, dass er den Job nicht bekommen hatte.
He had to come to terms with the fact that he had not gotten the job.
to compensate
To make a one-time payment to someone (a severance payment) in order to settle all further claims or demands, often as part of terminating a contract.
Das Unternehmen hat die entlassenen Mitarbeiter mit einer großzügigen Summe abgefunden.
The company compensated the dismissed employees with a generous sum.
'Abfinden' is a separable verb. The prefix 'ab' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er findet sich mit der Situation ab.
He comes to terms with the situation.
In the meaning of 'akzeptieren' (to accept), the verb is always reflexive and is used with the fixed preposition 'mit' and the dative. The structure is: sich mit etwas (Dativ) abfinden.
Sie musste sich mit dem Gedanken abfinden, umziehen zu müssen.
She had to come to terms with the idea of having to move.
In the meaning of 'entschädigen' (to compensate), the verb is transitive. You compensate someone (accusative), often with a sum of money. The structure is: jemanden (Akkusativ) mit etwas (Dativ) abfinden.
Nach der Kündigung fand die Firma ihn mit einer hohen Summe ab.
After the dismissal, the company compensated him with a large sum.
You can easily distinguish the two main meanings by the sentence structure. If the verb appears with the reflexive pronoun 'sich', it is about acceptance. If it appears with a person in the accusative as the object, it is about financial compensation.
Ich finde mich damit ab. (Akzeptanz)
I come to terms with it. (acceptance)
to accept / endure
Hinnehmen and sich abfinden mit both mean accepting an unpleasant situation without further resistance. Sich abfinden mit additionally shows that one regards the situation as unchangeable and gives up hope of changing it. Use hinnehmen more generally, and abfinden for reluctant resignation.
Sie musste sich damit abfinden, dass der Zug ausfiel.
She had to come to terms with the fact that the train had been canceled.
Sie musste die lange Wartezeit hinnehmen.
She had to put up with the long wait.
