O rendimento aumentou este mês.

Rendimento is a fairly broad noun. Depending on context, it can mean income, earnings, yield, return, or even performance.

So in a sentence like this, the exact English word depends on what is being talked about:

• money/salary/business: income / earnings / return
• school/work/sports: performance

O is the definite article, meaning the.

Portuguese uses definite articles more often than English does. Here, o rendimento refers to a specific income/yield/performance that the speaker has in mind. In standard Portuguese, leaving out the article would usually sound unnatural, except in very telegraphic styles like headlines.

Aumentou is the 3rd person singular of aumentar in the pretérito perfeito simples.

That means it describes a completed event or change:

• eu aumentei
• tu aumentaste
• ele/ela/você aumentou

In this sentence, the subject is o rendimento, so the singular form aumentou is used.

It can correspond to either one in English, depending on context.

In Portuguese, aumentou presents the increase as something that happened/completed. In English, with this month, people often say has increased this month, because the month is still ongoing. Portuguese still naturally uses aumentou here.

Este mês is the normal, direct way to say this month as a time expression.

Neste mês literally means in this month and is possible, but it usually sounds a bit more specific, contrastive, or tied to a bigger context. For a neutral sentence saying when something happened, este mês is the most natural choice.

In European Portuguese, este usually refers to something close to the speaker or to the present moment.

Since the sentence talks about the current month, este mês is the natural choice. Esse mês would normally refer to a month associated with the listener or a month already mentioned before.

The subject is o rendimento, which is singular, so the verb must also be singular: aumentou.

If the subject were plural, the verb would change too:

• Os rendimentos aumentaram este mês.

Yes. Portuguese allows some flexibility.

For example:

• O rendimento aumentou este mês.
• Este mês, o rendimento aumentou.

Both are correct. The second version puts more emphasis on this month.

Sometimes, yes, but the nuance may change.

• aumentou = the most neutral and general choice
• subiu = often used for prices, rates, numbers, values
• cresceu = often suggests growth or development

With rendimento, aumentou is a very safe and natural option.

Because mês is spelled with a circumflex accent in Portuguese: ê.

This marks the stressed vowel and is simply the correct spelling of the word month. A useful thing to notice is that the plural loses the accent:

• mês
• meses