fällig
due
Describes a debt or bill that must be paid at a certain time.
Die Miete ist immer am Ersten des Monats fällig.
The rent is always due on the first of the month.

due
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due
Describes a debt or bill that must be paid at a certain time.
Die Miete ist immer am Ersten des Monats fällig.
The rent is always due on the first of the month.

'Fällig' (due) is almost always used with the verb 'sein' (to be) or 'werden' (to become). The structure is typically: [something] ist/wird [when] fällig ([something] is/becomes due [when]).
Die nächste Rate für das Auto wird am Monatsende fällig.
The next installment payment for the car is due at the end of the month.
In financial contexts, 'fällig' (due) is often combined with obligations. Typical nouns are 'die Rechnung' (the bill), 'die Miete' (the rent), 'die Zahlung' (the payment), or 'der Beitrag' (the contribution/fee).
Der jährliche Mitgliedsbeitrag für den Sportverein ist fällig.
The annual membership fee for the sports club is due.
When it comes to expected events, 'fällig' (due) is often connected with regular appointments or maintenance. Common nouns are 'die Inspektion' (the inspection), 'die Prüfung' (the exam/check), or 'die Untersuchung' (the examination/check-up).
Die jährliche zahnärztliche Untersuchung ist mal wieder fällig.
The annual dental check-up is due again.
In this meaning, 'fällig sein' (to be due) is colloquial and expresses that a consequence or action is logical or deserved. It can be used for both positive and negative things.
Nach der harten Arbeit ist jetzt wirklich eine Pause fällig.
After the hard work, a break is really due now.
open
'offen' and 'fällig' can both occur with bills and debts. 'offen' means that a bill has not yet been paid. 'fällig' means that it must be paid now or by a specific date. Learners may confuse the words because both have to do with money. But the difference is important: a bill can already be due and still remain outstanding until you pay it.

Die Miete ist immer am ersten Tag des Monats fällig.
The rent is always due on the first day of the month.
Die Rechnung vom Handwerker ist noch offen.
The bill from the tradesperson is still outstanding.