Mi ne havas kontanton, do mi pagos per karto.

Because it is the direct object of havas.

In Esperanto, nouns normally end in -o:

• kontanto = cash

When a noun is the direct object, you add -n:

• Mi havas kontanton = I have cash

This is called the accusative ending. It shows what is being had, seen, bought, etc.

Ne is the normal word for not.

It usually goes right before the word or phrase being negated. In this sentence, it negates the whole idea of having cash, so it comes before the verb:

• Mi ne havas kontanton

That is the standard way to say I do not have cash.

In normal Esperanto, each clause usually has its own stated subject.

So:

• Mi ne havas kontanton, do mi pagos per karto.

Esperanto verbs do not change for person the way English does. Pagos only shows future tense; it does not by itself show I, you, he, etc. Because of that, the subject pronoun is usually necessary.

Leaving out the second mi would sound incomplete in ordinary prose.

Do means so, therefore, or thus.

It introduces a result or conclusion:

• Mi ne havas kontanton, do mi pagos per karto.

So the logic is:

1. I do not have cash.
2. Therefore, I will pay by card.

It is a very common connector in Esperanto.

The ending -os marks the future tense.

The verb is built like this:

• pagi = to pay
• pagas = pay / am paying
• pagis = paid
• pagos = will pay

So mi pagos means I will pay.

Because per shows the means or instrument used to do something.

So:

• per karto = by card / using a card

By contrast, kun usually means with in the sense of accompaniment:

• Mi venis kun amiko = I came with a friend

If you said kun karto, it could sound more like with a card in my possession, not necessarily using the card as the payment method. For method, per is the right choice.

Esperanto has no indefinite article.

English has:

• a card
• the card

Esperanto only has a definite article:

• la

So:

• karto can mean a card or just card depending on context
• la karto = the card

That is why per karto is perfectly normal.

Not exactly.

• mono = money in general
• kontanto = cash specifically

So this sentence is contrasting cash with card payment. That is why kontanto is the useful word here: it makes clear that the speaker does not have physical cash available.

Yes, Esperanto word order is fairly flexible, but the original order is the most straightforward and natural.

For example, you could also say:

• Mi pagos per karto, ĉar mi ne havas kontanton.

That changes the structure a little:

• ĉar = because
• do = so / therefore

So the original sentence gives the cause first and the result second. Both are natural; they just organize the information differently.