В конце месяца нам обещали аванс, поэтому я перестала волноваться из-за оплаты квартиры.

This means at the end of the month.

Two things are happening here:

• в конце = at the end / in the end part
• месяца is in the genitive because конец usually takes the genitive: конец чего? = the end of what?

So:

• в конце дня = at the end of the day
• в конце недели = at the end of the week
• в конце месяца = at the end of the month

This is a fixed and very common pattern in Russian.

Аванс usually means an advance payment.

In this sentence, it most likely means a salary advance: money paid before the full paycheck. So the idea is that they were expecting to receive some money before the month was over, and that made the speaker less worried about paying for the apartment.

Depending on context, аванс can also mean an advance payment in other situations, not only salary.

Russian often leaves out the subject when it is unknown, unimportant, or obvious from context.

So нам обещали аванс literally looks like:

• to us, [they] promised an advance

Here, обещали is 3rd person plural past tense, but the actual they is not specified. This is a very common Russian pattern, sometimes called an indefinite-personal construction.

It can sound natural in English as:

• we were promised an advance
• they promised us an advance

Russian often prefers this kind of subjectless plural when the focus is on the event, not on who exactly did it.

Because обещать normally works like to promise someone something.

So:

• обещать кому? = to promise to whom?
• обещать что? = to promise what?

In this sentence:

• нам = to us (dative)
• аванс = an advance (accusative, which looks like nominative here because it is inanimate masculine)

So:

• нам обещали аванс = they promised us an advance

Both can be possible in different contexts, but they are not exactly the same.

• обещали is imperfective
• пообещали is perfective

Here, обещали sounds like a neutral statement of fact: an advance had been promised. The focus is not strongly on the single completed act of making the promise, but on the existence of that promise as background information.

If you said нам пообещали аванс, it would sound more like:

• they made us a promise / they promised us once, as a completed act

So обещали fits well when the promise is just part of the situation that explains what happened next.

Перестала is the past tense of перестать and means stopped.

It also shows that the speaker is female.

In the past tense, Russian verbs agree with gender in the singular:

• я перестал = I stopped (male speaker)
• я перестала = I stopped (female speaker)

So this sentence tells us that the speaker is a woman.

Because перестать is perfective and is normally used for stopping something as a completed change.

• перестала волноваться = stopped worrying

This focuses on the moment/result of the change: before, she was worried; after that, she was not.

Переставала is imperfective and would usually need a different context, for example repeated or descriptive action:

• Она иногда переставала волноваться, а потом начинала снова. = Sometimes she would stop worrying, and then start again.

In your sentence, the perfective перестала is the natural choice.

Because Russian often uses an infinitive after verbs like start, continue, stop, want, can, and so on.

So:

• перестать волноваться = to stop worrying
• начать работать = to start working
• продолжать читать = to continue reading

This is a very normal structure: перестала + infinitive

Из-за here means something like because of, over, or on account of.

With emotional verbs like волноваться, it often means to worry about / over something:

• волноваться из-за денег = to worry about money
• волноваться из-за экзамена = to worry about the exam
• волноваться из-за оплаты квартиры = to worry about paying for the apartment / about the apartment payment

So the idea is not physical location or movement. It is the reason for the worry.

Because волноваться за and волноваться из-за are used differently.

• волноваться за кого-то / что-то often means being anxious for someone or something, often out of concern for their wellbeing
  • Я волнуюсь за ребёнка. = I’m worried about the child.
• волноваться из-за чего-то means worrying because of something, being upset over a reason/problem
  • Я волнуюсь из-за денег. = I’m worried because of money / about money.

In your sentence, the problem is the payment itself, so из-за is the natural choice.

First, из-за requires the genitive:

• из-за оплаты

So оплата becomes оплаты.

Then оплата itself usually takes the genitive for what is being paid for:

• оплата чего? = payment of what?
• оплата квартиры = payment for the apartment

So the structure is:

• из-за
  • genitive
• оплата
  • genitive

That gives:

• из-за оплаты квартиры

A literal breakdown would be something like: because of [the payment of the apartment]

In natural English, that usually becomes: about paying for the apartment or about the apartment payment

Not exactly, but in this context it can refer to something very close to that.

Оплата квартиры literally means payment for the apartment. Depending on the situation, it may mean:

• rent
• an apartment-related payment
• paying for the apartment in general

Russian can express this idea in several ways, for example:

• оплата квартиры
• оплата аренды
• квартплата (housing/utilities payment, depending on context)

So оплата квартиры is understandable and natural, though English may translate it more simply as rent if that fits the context.

Поэтому means therefore, so, or that’s why.

It connects the two parts logically:

• нам обещали аванс = we were promised an advance
• поэтому я перестала волноваться... = therefore / so I stopped worrying...

So the first part gives the reason, and the second part gives the result.

Russian word order is flexible, and the beginning of the sentence often sets the scene.

By starting with В конце месяца, the speaker puts the time frame first:

• At the end of the month, we were promised an advance...

This sounds natural because it tells you immediately when the important event happened or was expected.

Russian often moves time expressions to the front for emphasis or organization, even when English might not always do so.