Polisa osiguranja važi godinu dana.

Because osiguranja is the genitive singular form of osiguranje (insurance).

In Serbian, when one noun defines another, the second noun is often put in the genitive case. So:

• polisa = policy
• osiguranje = insurance
• polisa osiguranja = insurance policy

This is similar to saying policy of insurance, even though in natural English we say insurance policy.

Polisa is in the nominative singular because it is the subject of the sentence.

The verb važi agrees with it:

• polisa = singular
• važi = 3rd person singular present

So the structure is basically:

• Polisa osiguranja = the insurance policy
• važi = is valid
• godinu dana = for a year

Važi is the 3rd person singular present form of važiti.

In this sentence, it means:

• is valid
• remains valid
• is in effect

This verb is very common in Serbian and can also mean:

• to apply
• to count
• to be accepted
• to be true / hold

For example:

• To pravilo važi za sve. = That rule applies to everyone.
• Karta važi do petka. = The ticket is valid until Friday.

So here, važi is the natural verb for documents, tickets, policies, permits, and similar things.

This is a very common Serbian way to express duration.

• godinu = accusative singular of godina
• dana = genitive plural of dan

Together, godinu dana literally looks like a year of days, but idiomatically it simply means for a year or one year long.

This kind of expression is normal in Serbian:

• sat vremena = an hour
• nedelju dana = a week
• mesec dana = a month
• godinu dana = a year

You should learn these as set duration expressions.

Because Serbian often expresses duration without a preposition.

English says:

• for a year

Serbian usually just uses the accusative of duration:

• godinu dana

So the idea of for is already built into the case structure.

This is normal in Serbian:

• Čekao sam dva sata. = I waited for two hours.
• Živeli smo tamo godinu dana. = We lived there for a year.

You could, but godinu dana is much more natural here.

Compare:

• važi godinu dana = standard, idiomatic
• važi jednu godinu = understandable, but less natural in everyday Serbian

Jednu godinu may sound more emphatic or contrastive, as if you are stressing the number one.

In ordinary speech, durations like this are usually expressed with patterns such as:

• nedelju dana
• mesec dana
• godinu dana

This is a very important distinction.

• godinu dana = for a year / duration
• za godinu dana = in a year / after a year from now

So:

• Polisa osiguranja važi godinu dana. = The insurance policy is valid for a year.
• Polisa ističe za godinu dana. = The policy expires in a year.

The preposition za changes the meaning completely.

Sometimes yes, but the nuance is a little different.

• važi = is valid, is legally/institutionally in effect
• traje = lasts, continues for a period of time

For a policy, permit, visa, ticket, or contract, važi is usually the best choice because it focuses on validity.

Compare:

• Polisa osiguranja važi godinu dana. = The insurance policy is valid for a year.
• Sastanak traje dva sata. = The meeting lasts two hours.

You may hear traje godinu dana in some contexts, but for official validity, važi is more precise.

No, Serbian word order is fairly flexible, although the original version is the most neutral.

Neutral word order:

• Polisa osiguranja važi godinu dana.

Other possible orders:

• Godinu dana važi polisa osiguranja.
• Važi godinu dana polisa osiguranja.

These alternatives may sound more marked or stylistically unusual, depending on context. A learner should generally stick with:

• Polisa osiguranja važi godinu dana.

No. Serbian has no articles like English a/an/the.

So polisa osiguranja can mean:

• an insurance policy
• the insurance policy

The exact meaning depends on context.

If the sentence appears by itself, English may translate it either way depending on the situation.

Good question, because važi is present tense.

Present:

• Polisa osiguranja važi godinu dana.
• The insurance policy is valid for a year.

Past:

• Polisa osiguranja je važila godinu dana.
• The insurance policy was valid for a year.

Future:

• Polisa osiguranja će važiti godinu dana.
• The insurance policy will be valid for a year.

Notice the infinitive/past stem of the verb:

• važiti = to be valid
• važi = is valid
• važila = was valid
• će važiti = will be valid

Yes, godina is a feminine noun.

Its singular forms include:

• godina = nominative
• godinu = accusative

Because this sentence expresses duration, Serbian uses the accusative, so we get:

• godinu dana

This is a very common pattern with feminine nouns ending in -a:

• knjiga → knjigu
• škola → školu
• godina → godinu

This is part of a common Serbian quantity/duration pattern.

After words expressing a time span, Serbian often uses a noun in the genitive plural:

• pet dana = five days
• mesec dana = a month
• godinu dana = a year

So in godinu dana, the word dana is not the main time unit; it is part of an idiomatic duration phrase. You do not need to translate it literally every time. It is better to recognize the whole phrase as for a year.

You negate važi by adding ne:

• Polisa osiguranja ne važi godinu dana.

This means:

• The insurance policy is not valid for a year.

Depending on context, this could imply it is valid for a shorter or different period.

You might also hear more specific versions such as:

• Polisa osiguranja ne važi više. = The insurance policy is no longer valid.
• Polisa osiguranja ne važi u inostranstvu. = The insurance policy is not valid abroad.