По истечении трёх дней страховой депозит вернут.

Literally, по истечении means something like upon the expiration / after the lapse of something. So по истечении трёх дней means after three days have passed.

Yes, it is quite formal. You often see this kind of wording in contracts, hotel rules, rental agreements, and other official texts. In everyday speech, people would more often say через три дня or спустя три дня, depending on context.

Because по in this formal time expression takes the prepositional case, and the noun истечение becomes истечении.

So:

• dictionary form: истечение
• prepositional singular: истечении

This pattern is common in official Russian:

• по окончании = after the end of
• по прибытии = upon arrival
• по возвращении = upon return
• по истечении = after the expiration/lapse of

So по истечении is a set formal construction.

Because истечение requires the genitive case: it is the expiration of three days.

So the underlying structure is:

• истечение трёх дней = the expiration of three days

That is why both words are in forms that belong to the genitive phrase:

• трёх = genitive form of три
• дней = genitive plural of день

If you said три дня, that would just be the basic counting form, but here Russian needs of three days, not simply three days.

That is true in some contexts, but not here.

After 2, 3, 4, Russian often uses a form like:

• три дня
• четыре часа

That happens when the numeral phrase itself is in the basic nominative/accusative counting pattern.

But here the whole phrase is in the genitive, because it depends on истечение. Once the numeral phrase is declined, the noun no longer stays in that special counting form:

• nominative/accusative: три дня
• genitive: трёх дней

So трёх дней is exactly what you expect in this sentence.

It is the object, not the subject.

The verb вернут means will return in the sense of they will return. So the structure is basically:

• [They] will return the security deposit.

That means страховой депозит is the thing being returned, so it is the direct object.

A useful thing to notice is that for an inanimate masculine singular noun, the accusative looks exactly like the nominative. So страховой депозит could look like a subject at first glance, but here it is actually the object.

Because the verb is not agreeing with страховой депозит. The hidden subject is an unspecified they.

Russian often uses 3rd person plural with no stated subject to mean something like:

• they will return it
• someone will do it
• it will be done

So страховой депозит вернут literally means they will return the security deposit, but in natural English we often translate that as the security deposit will be returned.

This is called an indefinite-personal construction, and it is very common in Russian.

Russian often prefers an active verb with an unspecified they where English would naturally use the passive.

So these are both possible:

• Страховой депозит вернут.
• Страховой депозит будет возвращён.

Both mean roughly the same thing: The security deposit will be returned.

The version with вернут is concise and very natural in Russian. The passive version будет возвращён is also correct, but it sounds a bit more explicitly formal/bookish.

So the sentence you were given is a very normal Russian way to express this idea.

Вернут is the future tense of the perfective verb вернуть.

That matters because in Russian:

• perfective future = one completed action in the future
• imperfective future = ongoing, repeated, or process-focused future action

So вернут means they will return it as a completed act.

It is a simple future form, not a compound one. That is why there is no будут here.

Compare:

• вернут = they will return it / they will give it back
• будут возвращать = they will be returning it / will return it repeatedly or as a process

In this sentence, the completed future action is what we want.

Страховой депозит is understandable and fairly common in formal or commercial contexts, especially in rental, hotel, or service-related language. It usually corresponds to security deposit.

In everyday speech, though, people often say залог instead, depending on the situation.

For example:

• нужно оставить залог = you need to leave a deposit
• страховой депозит = security deposit, often a more formal/official term

So страховой депозит is not wrong at all, but it sounds more administrative or contractual than casual.

Also, despite the adjective страховой, this does not usually mean an insurance payment in this context. It means a deposit kept as financial security.

Yes. Russian word order is flexible.

This sentence puts the time expression first:

• По истечении трёх дней страховой депозит вернут.

That sounds natural because it highlights the condition/time frame first: after three days.

You could also say:

• Страховой депозит вернут по истечении трёх дней.

The meaning stays basically the same. The difference is mostly in emphasis:

• first position = highlights the timing
• later position = highlights the deposit first

In formal notices, putting the time condition first is very common.

Because Russian often omits subject pronouns when they are not needed.

In this sentence, Russian does not say они вернут, because the verb form вернут already shows 3rd person plural. And since the exact people do not matter, leaving the subject unstated is completely normal.

So the sentence does not mean that actual specific they are important. It just means that the action will be carried out by whoever is responsible.

That is one reason Russian often sounds more concise than English in sentences like this.