A pénzügyi terv az e-mailben van.

A is the Hungarian definite article, meaning the.

So:

• A pénzügyi terv = the financial plan

Hungarian uses definite articles a lot like English does, but the form changes depending on the next word:

• a before most consonant sounds
• az before vowel sounds

That is why you get:

• A pénzügyi terv
• az e-mailben

Because e-mailben starts with a vowel sound, Hungarian uses az instead of a.

Compare:

• a ház = the house
• az autó = the car
• az e-mail = the email

So az e-mailben means in the email.

Pénzügyi means financial.

It is an adjective, and in Hungarian adjectives normally come before the noun, just like in English:

• pénzügyi terv = financial plan
• nagy ház = big house
• jó ötlet = good idea

So the structure is straightforward for an English speaker:

• pénzügyi = financial
• terv = plan

Together: pénzügyi terv = financial plan

-ben is a case ending meaning in or inside.

So:

• e-mailben = in the email
• házban = in the house
• szobában = in the room

Hungarian often expresses ideas like in, on, to, from, etc. by adding endings to nouns instead of using separate prepositions.

That means English in the email becomes:

• az e-mailben

This is because of vowel harmony, a major feature of Hungarian.

The inessive ending has two common forms:

• -ban
• -ben

Very roughly:

• words with back vowels usually take -ban
• words with front vowels usually take -ben

Since e-mail is treated as taking the front-vowel version, it becomes:

• e-mailben

A simple comparison:

• házban = in the house
• kertben = in the garden
• e-mailben = in the email

Loanwords do not always feel perfectly predictable at first, so this is something learners often just get used to through exposure.

That is a very common and very good question.

Hungarian often omits van in the present tense when saying that something is something:

• A terv jó. = The plan is good.
• Ő tanár. = He/She is a teacher.

But when you say that something exists somewhere or is located somewhere, Hungarian usually does use van:

• A könyv az asztalon van. = The book is on the table.
• A pénzügyi terv az e-mailben van. = The financial plan is in the email.

So here van is needed because the sentence is about location.

That is the most neutral word order here.

Hungarian word order is flexible, but it is strongly connected to focus and emphasis. In a neutral sentence about location, the verb often comes at or near the end:

• A pénzügyi terv az e-mailben van.

This sounds like a plain statement: The financial plan is in the email.

Hungarian does not always follow a fixed English-style word order. Instead, speakers move parts of the sentence around to highlight different information.

Yes, absolutely.

Both are grammatical, but the emphasis is a little different.

• A pénzügyi terv az e-mailben van.
  Neutral statement about where the financial plan is.

• Az e-mailben van a pénzügyi terv.
  Puts more attention on where it is: It’s in the email that the financial plan is.

In real conversation, Hungarian speakers often move sentence parts around depending on what is already known and what is new or important.

Usually az e-mailben van suggests that the information is in the body/text of the email.

If you want to make it clear that something is in an attachment, Hungarian would usually say something more specific, for example:

• A pénzügyi terv a csatolmányban van. = The financial plan is in the attachment.

So if someone says:

• A pénzügyi terv az e-mailben van.

the most natural interpretation is that you can find it in the message.

It is a borrowed word, but it is very common in Hungarian.

You may see:

• e-mail
• email

Both are used. Hungarian often adds its normal endings to borrowed words:

• e-mailben = in the email
• e-mailt = email (object form)
• e-mailre = onto/for the email, depending on context

So even though the word comes from English, it behaves like a regular Hungarian noun in many ways.

It is in the inessive case.

The inessive case expresses the idea of in or inside. Its endings are:

• -ban
• -ben

So:

• e-mailben = in the email
• szobában = in the room
• dobozban = in the box

If you are learning Hungarian grammar terminology, this is a useful case to recognize because it appears very often.

A rough learner-friendly pronunciation is:

ah PAYN-zue-dyee terv az EE-mayl-ben von

A few notes:

• A sounds like a short aw/uh sound, not the English letter name ay
• pénzügyi is the trickiest word; the gy is a soft Hungarian consonant
• e-mailben is roughly EE-mayl-ben
• van is pronounced more like von than English van

Also, Hungarian stress is usually on the first syllable of each word:

• A PÉNzügyi TERV az E-mailben VAN

No. In this sentence, pénzügyi stays the same.

Hungarian adjectives do not change for gender, and they usually do not change to agree with the noun the way they do in languages like German, French, or Spanish.

So:

• pénzügyi terv = financial plan
• pénzügyi jelentés = financial report
• pénzügyi adatok = financial data

The adjective stays pénzügyi regardless of the noun.

Because Hungarian often uses suffixes where English uses prepositions.

English says:

• in the email

Hungarian says:

• az e-mailben

That breaks down as:

• az = the
• e-mail = email
• -ben = in

This is one of the biggest structural differences between English and Hungarian. Instead of putting a small word before the noun, Hungarian often adds an ending directly to the noun.