Sparnaðurinn okkar hjálpar okkur að borga leiguna ef útborgunin kemur seint.

Because sparnaður is often used as a singular mass noun in Icelandic. English commonly uses the plural noun savings, but Icelandic can express the same idea with singular sparnaður.

So:

• sparnaður = savings / saving / thrift
• sparnaðurinn = the savings

Since the subject is singular, the verb is singular too:

• Sparnaðurinn okkar hjálpar ... = Our savings help ...

That is why you get hjálpar and not a plural verb form.

It is the suffixed definite article, meaning the.

Icelandic usually attaches the to the end of the noun instead of writing it as a separate word.

So:

• sparnaður = savings / saving
• sparnaðurinn = the savings

The same thing happens later in the sentence:

• leiguna = the rent
• útborgunin = the payout/payment

In Icelandic, a very common way to say possession is:

noun + definite article + possessive pronoun

So:

• sparnaðurinn okkar = our savings
• literally: the savings of ours

This is a normal everyday pattern:

• bíllinn minn = my car
• húsið okkar = our house

So sparnaðurinn okkar sounds natural and standard.

Because Icelandic pronouns change form depending on grammatical case.

These are different forms of the same pronoun family:

• við = we
• okkur = us (dative/accusative form in many contexts; here dative)
• okkar = our / of us (genitive)

So:

• sparnaðurinn okkar = our savings
• hjálpar okkur = helps us

English uses separate words like our and us, and Icelandic does the same idea through case forms.

Because the verb hjálpa takes the dative case.

The pattern is:

hjálpa einhverjum = to help someone

So:

• hjálpa mér = help me
• hjálpa þér = help you
• hjálpa okkur = help us

This is something Icelandic learners often need to memorize with verbs: many verbs require a specific case for their object.

Here að is the infinitive marker, like English to.

So:

• borga = pay
• að borga = to pay

In this sentence:

• hjálpar okkur að borga leiguna = helps us pay / helps us to pay the rent

This að is not functioning as a preposition here; it is just introducing the infinitive.

Because leiguna is the definite object form: the rent.

The base noun is:

• leiga = rent

But here it is the direct object of borga, so it appears in the accusative, and it is definite:

• leiguna = the rent

So the sentence is specifically talking about paying the rent, not just rent in a general sense.

Útborgun can mean a payout, payment, disbursement, or in some contexts something like a paycheck/payday payment. The exact English word depends on the situation.

In this sentence, it means the money payment that is expected to arrive. Since the form is definite:

• útborgunin = the payout / the payment

So the idea is that this expected payment may arrive late.

Because Icelandic often uses koma (come/arrive) for things that arrive late, including payments, buses, letters, and people.

So:

• útborgunin kemur seint = the payment comes late / arrives late

Also, seint is an adverb meaning late, and it modifies the verb kemur.

This is a very natural Icelandic way to express lateness of arrival.

The sentence has a main clause plus an if-clause.

Main clause:

• Sparnaðurinn okkar hjálpar okkur að borga leiguna

Subordinate clause:

• ef útborgunin kemur seint

In the main clause, Icelandic normally follows a verb-second pattern. Here the subject comes first, so the finite verb comes second:

• Sparnaðurinn okkar
  • hjálpar

After ef (if), the clause has normal subordinate-clause order:

• útborgunin
  • kemur
    • seint

If you put the if-clause first, the main clause still keeps verb-second order:

• Ef útborgunin kemur seint, hjálpar sparnaðurinn okkar okkur að borga leiguna.

Yes:

• Sparnaðurinn okkar — nominative subject, our savings
• hjálpar — present tense, 3rd person singular of hjálpa
• okkur — dative, us
• að borga — infinitive phrase, to pay
• leiguna — accusative definite object, the rent
• ef — if
• útborgunin — nominative subject of the subordinate clause, the payout/payment
• kemur — present tense, 3rd person singular of koma
• seint — adverb, late

So this one sentence shows several very common Icelandic features at once: attached definite articles, case forms, possessive pronouns, infinitives with að, and an ef subordinate clause.