Nach der Funktionsprüfung zahle ich einen freiwilligen Beitrag.

Because nach takes the dative case in this meaning.

• nach = after
• Funktionsprüfung is a feminine noun: die Funktionsprüfung
• Feminine singular in the dative is der Funktionsprüfung

So:

• nominative: die Funktionsprüfung
• dative after nach: nach der Funktionsprüfung

This is a very common pattern in German:

• nach dem Essen = after the meal
• nach der Arbeit = after work
• nach dem Test = after the test

Here, nach means after in a time sense.

So nach der Funktionsprüfung means after the functional test / after the inspection / after the functionality check, depending on context.

Be careful: nach can have other meanings too, such as:

• to or towards with cities/countries: Ich fahre nach Berlin.
• according to: nach dem Plan
• for in expressions like nach etwas suchen does not work; German uses different structures there

But in this sentence, it is clearly temporal: after.

Because German main clauses follow the verb-second rule.

That means the finite verb must be in the second position, not necessarily the second word.

Here, the first position is occupied by the time phrase:

• Nach der Funktionsprüfung = position 1

So the verb must come next:

• zahle = position 2

Then comes the subject:

• ich

So the structure is:

• Nach der Funktionsprüfung | zahle | ich | einen freiwilligen Beitrag

If you started with the subject instead, that would also be correct:

• Ich zahle nach der Funktionsprüfung einen freiwilligen Beitrag.

Both are grammatical. The version with Nach der Funktionsprüfung first puts more emphasis on the timing.

Because Beitrag is masculine: der Beitrag, and it is the direct object of zahlen, so it is in the accusative case.

That gives:

• nominative: der Beitrag
• accusative: einen Beitrag

The adjective also changes its ending:

• ein freiwilliger Beitrag = nominative
• einen freiwilligen Beitrag = accusative masculine

So both words show the case:

• einen = masculine accusative article
• freiwilligen = adjective ending for that pattern

Because adjectives placed before nouns usually take an ending in German.

Here the adjective comes after einen, so it must agree with:

• gender: masculine
• number: singular
• case: accusative

That produces:

• einen freiwilligen Beitrag

Compare:

• ein freiwilliger Beitrag = a voluntary contribution
• ich zahle einen freiwilligen Beitrag = I pay a voluntary contribution
• mit einem freiwilligen Beitrag = with a voluntary contribution

So the adjective ending changes depending on the grammar around it.

Yes. Funktionsprüfung is a compound noun, and German uses these very often.

It is made from:

• Funktion = function
• Prüfung = test, examination, inspection, check

Together, Funktionsprüfung means something like:

• functionality test
• functional test
• inspection of function

The last part, Prüfung, is the main noun, so it determines the gender. Since die Prüfung is feminine, die Funktionsprüfung is also feminine.

That -s- is a linking element often called a Fugen-s.

German compounds sometimes insert an s between parts:

• Funktion + Prüfung → Funktionsprüfung
• Arbeitszimmer
• Lebensmittel
• Hochzeitsfeier

There is not always a simple rule that lets you predict it perfectly, so learners usually pick it up word by word. The important thing is that Funktionsprüfung is the correct standard form.

In German, the present tense can cover several meanings that English often separates.

So ich zahle can mean:

• I pay
• I am paying
• I will pay

The exact meaning depends on context.

In this sentence, because of nach der Funktionsprüfung, it often sounds like a future or planned action:

• After the functional test, I will pay a voluntary contribution.

But grammatically, it is simply present tense: ich zahle.

Beitrag usually means a contribution or payment toward something.

It can be used in different contexts:

• club membership fee
• financial contribution
• contribution to costs
• article/contribution in a magazine or discussion

In this sentence, because of freiwilligen, it means a voluntary contribution/payment, not a fixed required fee.

That makes it different from words like:

• Gebühr = fee, charge
• Spende = donation
• Beitrag = contribution, often somewhat neutral or institutional

So freiwilliger Beitrag suggests a payment that is not strictly required.

Yes, absolutely.

Both are correct:

• Nach der Funktionsprüfung zahle ich einen freiwilligen Beitrag.
• Ich zahle nach der Funktionsprüfung einen freiwilligen Beitrag.

The difference is mainly emphasis:

• starting with Nach der Funktionsprüfung highlights when
• starting with Ich is more neutral

German is flexible, but the finite verb still has to stay in second position in a main clause.

Because a simple adverbial phrase at the beginning of a German main clause normally does not need a comma.

So this is correct:

• Nach der Funktionsprüfung zahle ich einen freiwilligen Beitrag.

A comma would usually appear only in other structures, such as subordinate clauses or inserted phrases, not after a normal fronted time expression.

In this sentence, the capitalized words are nouns:

• Funktionsprüfung
• Beitrag

German capitalizes all nouns, not just proper names.

So compare:

• freiwilligen = adjective, not capitalized
• Beitrag = noun, capitalized

This is one of the most visible spelling differences between German and English.