to debit / write off
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to debit
To deduct or charge an amount of money from an account, usually as part of a bank transfer, direct debit, or card payment.
Die monatliche Rate für das Auto wird immer am Ersten des Monats abgebucht.
The monthly installment for the car is always debited on the first of the month.
'Abbuchen' (to debit / write off) is a separable verb. The prefix 'ab-' stands at the end in a main clause, while it remains connected to the verb in a subordinate clause. In the infinitive with 'zu', 'zu' stands between the prefix and the verb.
Die Bank bucht die Gebühr monatlich ab.
The bank debits the fee monthly.
When stating where the money is taken from, you use the preposition 'von' (from) with the dative. The verb is also very often used in the passive to describe the process.
Der Betrag wird von meinem Konto abgebucht.
The amount is debited from my account.
In a financial context, 'abbuchen' (to debit) is often combined with nouns such as 'Geld' (money), 'ein Betrag' (an amount), 'die Miete' (the rent), or 'eine Rechnung' (an invoice).
Jeden Monat wird die Miete automatisch von meinem Konto abgebucht.
Every month, the rent is automatically debited from my account.
The figurative meaning of considering something finished or lost is colloquial. It is used to express that one has given up on a goal or a hope.
Nach dem schlechten Start können wir das Projekt wohl abbuchen.
After the bad start, we can probably write off the project.
to give up / submit
'aufgeben' and 'abbuchen' can be similar when you no longer pursue something. 'aufgeben' directly says that you stop an attempt, plan, or hope. 'abbuchen' is used figuratively and colloquially here: you regard something as done, lost, or a failure and do not think about it any further. 'aufgeben' works well when an active attempt is still the focus. 'abbuchen' sounds more as if you are mentally drawing a line under something.
Julian hat den verpassten Termin als Pech abgebucht und einen neuen vereinbart.
Julian wrote off the missed appointment as bad luck and arranged a new one.
Nach zwei Stunden Suche gab Lisa den verlorenen Schlüssel auf.
After two hours of searching, Lisa gave up on the lost key.