Learn Hardcore Russian: Я иду в банк, чтобы заплатить за квартиру. - I am going to the bank in order to pay for the apartment.

идти – imperfective, one-direction, in progress / very near future.
Я иду в банк = I’m going (right now / I’m on my way) to the bank.
пойти – perfective, one-direction, start of the movement / intention.
Я пойду в банк = I will go to the bank (at some point, I’ll set off).

In this context, иду suggests you are already on your way (or it’s happening right now / very imminently), which fits well with the English I’m going to the bank….
If you said Я пойду в банк, чтобы заплатить за квартиру, it would sound more like I’ll go to the bank to pay the rent (a future plan, not necessarily happening at this moment).

Why is it в банк and not в банке?

The difference is:

в банк – accusative, direction: to the bank (where you are going).
в банке – prepositional, location: in/at the bank (where you are).

Your sentence describes movement towards a place:

Я иду в банк = I’m going to the bank. (direction)

If you were already there, you would say:

Я в банке = I’m at the bank. (location)

Why is there no word for the in в банк or за квартиру?

Russian has no articles at all—no a/an and no the.
Context tells you whether it’s a bank or the bank.

в банк can mean to a bank or to the bank.
за квартиру can mean for an apartment or for the apartment (usually for the apartment rent).

So you don’t add anything like the; you just say в банк, за квартиру, etc.

What does чтобы mean here, and why do we need it?

чтобы introduces a purpose clause and corresponds to in order to / so as to in English.

Я иду в банк, чтобы заплатить за квартиру.
= I’m going to the bank in order to pay for the apartment.

Structure:

чтобы + infinitive (perfective or imperfective) when subject is the same:
Я иду, чтобы заплатить…

Without чтобы, Я иду в банк заплатить за квартиру is possible in speech, but more colloquial and a bit rougher stylistically. The standard, neutral version is with чтобы.

Why is it заплатить and not платить?

This is about verb aspect:

платить – imperfective: process, repeated action, to pay (in general).
заплатить – perfective: single, completed action, to pay (once, to finish paying).

Here you are describing one concrete action you want to complete (pay the rent once this time), so Russian uses the perfective:

чтобы заплатить за квартиру = in order to pay (the rent completely).

If you said чтобы платить за квартиру, it would sound more like:

in order to be paying for the apartment (regularly) – describing an ongoing or repeated obligation, which is not what the sentence is about.

Why is it за квартиру and not для квартиры?

Different prepositions, different meanings:

платить / заплатить за + accusative = to pay for (something as an object/service that costs money)
- заплатить за квартиру = to pay for the apartment (i.e. the rent).
- заплатить за учебу = to pay for tuition.
для + genitive = for (intended for the use/benefit of someone/something)
- для квартиры = for the apartment (e.g. something intended for the apartment).

So:

заплатить за квартиру – pay for the apartment (money to landlord).
купить мебель для квартиры – buy furniture for the apartment (intended for that place).

Why is квартиру in the accusative case (-у)?

Because the verb платить / заплатить with the preposition за requires accusative for the thing you are paying for:

платить за что? – за квартиру, за еду, за билеты … (all accusative).

So квартира (nominative) → квартиру (accusative), following the pattern of feminine nouns ending in -а:

квартира → квартиру
машина → машину
работа → работу

Does за квартиру literally mean for the apartment, or specifically for the rent?

Literally, за квартиру is for the apartment, but in everyday Russian this phrase very commonly means “for the rent” (payment for living there).

Context usually makes it clear:

заплатить за квартиру – almost always understood as pay the rent.
If you wanted to be extra clear, you could say заплатить за аренду квартиры, but that’s often unnecessary in normal conversation.

Could I say Я иду платить за квартиру в банк instead?

You can hear Я иду платить за квартиру в банк in spoken Russian, but it’s less clear and less standard:

Without чтобы, идти + infinitive is colloquial and can sound a bit rough or hurried.
Also, placing в банк at the end can momentarily confuse the listener (it might be parsed as to pay for an apartment in the bank before they reinterpret it).

The most natural, clear, and neutral is:

Я иду в банк, чтобы заплатить за квартиру.

Other acceptable variants:

Я иду платить за квартиру в банк (colloquial, sounds more spoken).
Я иду в банк платить за квартиру (still colloquial, but a bit clearer).

Why is there a comma before чтобы?

In Russian, чтобы often introduces a subordinate clause of purpose, which is separated by a comma:

Я иду в банк, чтобы заплатить за квартиру.

Think of it like:

I’m going to the bank, (in order) to pay for the apartment.

The comma marks off the main clause (Я иду в банк) from the purpose clause (чтобы заплатить за квартиру). This is a standard punctuation rule.

Can I omit я and just say Иду в банк, чтобы заплатить за квартиру?

Yes, in spoken Russian it’s possible to drop я:

Иду в банк, чтобы заплатить за квартиру.

Russian often omits personal pronouns when the subject is clear from the verb ending. Иду can only refer to я in this context, so it’s understood.

However:

Including Я (Я иду…) is the neutral and slightly more explicit version.
Dropping Я sounds a bit more casual or narrative (e.g. when telling a story, writing notes, texting).

What is the difference between идти and ходить, and could I say Я хожу в банк, чтобы заплатить за квартиру?

идти vs ходить:

идти – one-direction, this specific trip, in progress or very near future.
Я иду в банк = I’m going (now) to the bank.
ходить – multidirectional, habitual / repeated action or movement in various directions.
Я хожу в банк = I go to the bank (regularly, as a habit).

So:

Я иду в банк, чтобы заплатить за квартиру.
= This particular time, you’re going to pay the rent now.
Я хожу в банк, чтобы заплатить за квартиру.
= I (regularly) go to the bank to pay the rent. (habitual action, e.g. every month).

Can иду here also refer to the near future, like I’m going to go to the bank (soon), not literally right this second?

Yes. Russian present tense of verbs of motion like идти is often used for very near future plans, similar to English I’m going to the bank (later today) if it’s arranged or imminent.

Context decides:

Said while already walking: literally I’m going now.
Said earlier in the day: I’m (definitely) going to the bank (today/soon) to pay the rent.

If you want a more generic or less immediate future, you’d typically use пойду (future) or something like Я собираюсь пойти в банк… (I’m planning to go to the bank…).