Quieren acabar de pagar la hipoteca pronto para no vivir siempre con esa preocupación.

Quieren is the 3rd person plural form of querer, so it means they want.

Spanish often omits subject pronouns when the verb ending already makes the subject clear. So:

• Quieren acabar... = They want to finish...
• Ellos quieren acabar... is also possible, but ellos is usually only added for emphasis, contrast, or clarity.

After verbs like querer, poder, deber, pensar, and many others, Spanish normally uses a second verb in the infinitive.

So:

• quieren pagar = they want to pay
• quieren acabar de pagar = they want to finish paying

This is very similar to English want to pay, except Spanish does not use a separate word for to before the infinitive in this structure.

In this sentence, it means to finish paying / to pay off.

This is a very common learner question because acabar de + infinitive often means to have just done something:

• Acabo de comer = I’ve just eaten

But in this sentence, the context makes that impossible:

• Quieren acabar de pagar la hipoteca pronto = they want to finish paying the mortgage soon

So here, acabar de pagar is understood as finish paying off.

A natural English equivalent is:

• to pay off the mortgage

Yes, absolutely. Terminar de pagar is also very natural and means basically the same thing here:

• Quieren terminar de pagar la hipoteca pronto...

Both can mean to finish paying off.

The reason learners notice acabar de pagar more is that acabar de + infinitive also has the other meaning of to have just done something, so context matters. In this sentence, pronto and quieren clearly point to the finish paying meaning.

La hipoteca means the mortgage.

In everyday Spanish, especially in normal conversation, hipoteca usually refers to the mortgage as a financial burden or loan on a home.

So:

• pagar la hipoteca = pay the mortgage
• acabar de pagar la hipoteca = finish paying off the mortgage

Yes, pronto can move around somewhat, but its position here is very natural:

• Quieren acabar de pagar la hipoteca pronto...

It modifies the idea of finishing paying, so placing it after la hipoteca sounds smooth and normal.

Other possible placements are:

• Quieren pronto acabar de pagar la hipoteca... → possible, but less natural in everyday speech
• Pronto quieren acabar de pagar la hipoteca... → possible in a specific context, but marked

So the original word order is the most neutral and idiomatic.

Because para + infinitive is used when the purpose involves the same subject as the main verb.

Here, the people who want something are the same people who would live with that worry:

• Quieren acabar de pagar... para no vivir...
• They want to finish paying... so as not to live...

If the subject changed, Spanish would normally use para que + subjunctive instead.

For example:

• Quieren acabar de pagar la hipoteca para que sus hijos vivan más tranquilos.
• They want to finish paying the mortgage so that their children can live more peacefully.

In Spanish, no normally goes directly before the verb it negates.

So:

• no vivir = not to live
• para no vivir siempre con esa preocupación = so as not to always live with that worry

This is the standard pattern with infinitives too:

• no comer
• no pagar
• no salir

Yes, siempre literally means always, but in this sentence it has the broader everyday sense of:

• constantly
• all the time
• forever / indefinitely, depending on context

So here it suggests the idea of not wanting to go on living with that worry year after year.

It does not have to mean mathematically every single moment. It is a very natural way to express a continuing burden.

Because Spanish often expresses this idea with the noun preocupación:

• vivir con una preocupación = to live with a worry / concern
• vivir preocupado = to live worried

Both are possible, but they are slightly different in feel:

• vivir con esa preocupación focuses on the burden/problem they carry
• vivir preocupados focuses more on their emotional state

So the original sentence highlights the mortgage as an ongoing source of worry.

Esa means that, while esta means this.

In sentences like this, esa preocupación often refers to a worry that is being treated as something already understood, known, or mentally a bit more distant:

• the worry of still having the mortgage
• that particular concern

Using esta would feel a little closer or more immediate. In many contexts, both could be grammatically possible, but esa preocupación sounds very natural here.

Usually worry or concern fits best here.

• worry sounds very natural in everyday English
• concern is slightly more neutral or formal
• anxiety is usually stronger and more emotional

So in this sentence, esa preocupación is most naturally understood as:

• that worry
• that concern

Yes. In this context, acabar de pagar la hipoteca is very close to pay off the mortgage.

A few useful comparisons:

• pagar la hipoteca = pay the mortgage
  (make mortgage payments)
• acabar de pagar la hipoteca = finish paying the mortgage / pay off the mortgage
  (complete all the payments)

So if an English speaker wants the most natural equivalent, pay off the mortgage is often the best choice.