Grundpreis und Arbeitspreis bestimmen die Nachzahlung.

Because the subject is compound: Grundpreis und Arbeitspreis = the base price and the usage price.

Two nouns joined by und usually make a plural subject, so the verb must be in the plural:

• der Grundpreis bestimmt = the base price determines
• der Grundpreis und der Arbeitspreis bestimmen = the base price and the usage price determine

So bestimmen is the correct 3rd person plural form.

German main clauses usually follow the verb-second rule: the finite verb comes in the second position.

Here the sentence structure is:

• Grundpreis und Arbeitspreis = subject
• bestimmen = finite verb
• die Nachzahlung = object

So the basic order is:

Subject + Verb + Object

That gives:

Grundpreis und Arbeitspreis bestimmen die Nachzahlung.

This is very normal German word order.

Die Nachzahlung is in the accusative case, because it is the direct object of bestimmen.

The verb bestimmen here means to determine or to decide what something will be, and the thing being determined is die Nachzahlung.

A useful way to think about it:

• Who/what determines? → Grundpreis und Arbeitspreis
• What do they determine? → die Nachzahlung

Since Nachzahlung is a feminine noun, the article die is the same in both nominative and accusative, so the article alone does not show the case clearly. You identify the case mainly from the sentence function.

These are both very common billing/utility terms in German.

• Grundpreis = base price, fixed basic charge
• Arbeitspreis = unit rate, usually the price for actual consumption, such as electricity, gas, or water used

So in many real-world contexts:

• Grundpreis = what you pay anyway
• Arbeitspreis = what you pay based on usage

Together, they help determine the final amount you still owe or get billed for.

Not quite. Nachzahlung is more specific than just payment.

It usually means an additional payment, back payment, or amount still owed after calculation.

Typical situation:

• you have already paid some estimated amounts during the year
• then the final bill is calculated
• if you have paid too little, you must make a Nachzahlung

So Nachzahlung is often the extra amount you need to pay afterward.

The opposite idea is often:

• Rückzahlung = refund / money paid back to you

German often leaves out articles in general statements, especially when talking about things in a broad, abstract, or category-like way.

So:

• Der Grundpreis und der Arbeitspreis bestimmen die Nachzahlung.
  = more explicit, fully marked

• Grundpreis und Arbeitspreis bestimmen die Nachzahlung.
  = also natural, especially in explanatory, technical, or billing language

Leaving out the articles can sound a bit more formal, headline-like, or technical.

Each word is singular:

• Grundpreis = one base price
• Arbeitspreis = one usage rate

But because there are two singular nouns joined by und, together they form a plural subject. That is why the verb is plural:

• Grundpreis bestimmt ...
• Arbeitspreis bestimmt ...
• Grundpreis und Arbeitspreis bestimmen ...

Yes. In this context, bestimmen is a very natural choice for determine, decide, or set.

Here it means something like:

• these two factors determine the amount of the additional payment
• these two components decide what the additional payment will be

In billing or calculation contexts, bestimmen works very well.

Yes, German allows different word orders for emphasis, as long as the finite verb stays in second position in a main clause.

For example:

Die Nachzahlung bestimmen Grundpreis und Arbeitspreis.

This is grammatically correct, but it puts more focus on die Nachzahlung. It may sound more marked or stylistic than the original.

The original version is the most neutral:

Grundpreis und Arbeitspreis bestimmen die Nachzahlung.

Yes, all three important nouns are compound nouns, which is very common in German.

Breakdown:

• Grundpreis = Grund

  • Preis
    literally something like basic/fundamental price

• Arbeitspreis = Arbeit

  • Preis
    literally work price, but in real usage it means the consumption-based rate

• Nachzahlung = nach

  • Zahlung
    literally after-payment or payment afterward

A helpful tip for German learners: when you see a long noun, look at the last part first. The last part is the main noun:

• Preis tells you the first two are types of price
• Zahlung tells you the last one is a type of payment

A rough pronunciation guide is:

GRUNT-price oont AR-bite-price beh-SHTIM-men dee NAHK-tsah-loong

A few useful points:

• und often sounds more like unt in normal speech
• ei in Arbeitspreis sounds like English eye
• st in bestimmen is pronounced sht
• z in Nachzahlung sounds like ts
• ch in Nach is the hard kh sound, like in Scottish loch

So the rhythm is roughly:

GRUNDpreis und ARbeitspreis bestimmen die NACHzahlung.

The main stress is usually on the first syllable of each compound:

• GRUNDpreis
• ARbeitspreis
• NACHzahlung