Ég hef ekki borgað dagsektina, þótt lánstíminn sé útrunninn.

Questions & Answers about Ég hef ekki borgað dagsektina, þótt lánstíminn sé útrunninn.

Since the current lesson is about ditransitive verbs, why is dagsektina in the accusative case here instead of the dative?
The verb borga (to pay) is ditransitive, but it isn't a double dative verb. It takes a dative receiver (the person you pay) and an accusative object (the thing or amount you pay). Because dagsektina (the daily fine) is the thing being paid, it takes the accusative. If you added a person, they would take the dative, as in Ég hef ekki borgað honum dagsektina (I have not paid him the daily fine).
Why do we use the subjunctive sé instead of the regular indicative er here?
The conjunction þótt (although) strictly triggers the subjunctive mood in Icelandic. Because of this, the regular present tense er (is) must change to its subjunctive form sé. You would also use the subjunctive if you used the synonymous phrase þó að.
Why does the adjective útrunninn end in a double -nn?
The word útrunninn (expired or run out) describes lánstíminn (the loan period). Because tími is a masculine noun acting as the subject of the clause, it is in the nominative case. The describing word must agree with it, and the masculine nominative singular form of this participle ends in -inn.
Why does the compound word lánstíminn have an -s- in the middle, while dagsektina does not?
Compound words in Icelandic are glued together in a few different ways. Lánstíminn connects lán (loan) and tími (time) using the genitive -s, functioning a bit like a possessive (time of the loan). Meanwhile, dagsekt connects dagur (day) and sekt (fine) using just the root of the first word (dag-), which is common when the first word simply acts as a broad category.

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