Consider this sentence:
My cousin lent me his camera for two days.
Which of the following constructs would be more natural and why:
1. Mi primo me prestó su cámara por dos días.
2. Mi primo me prestó su cámara para dos días.
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In this case por is the correct answer. You could substitute it for durante in this context, and you use it to talk about periods of time. Since I'm from Spain, durante sounds more natural in this case, but in some countries of Latin America they'd use por more naturally.
You'd use para to talk about the reason why the camera was lent to you. E.g. me dejó la cámara para sacar fotos (he lent me his camera to take pictures).
I can't give you a particular rule to choose between para and por, they are similar to on, in and at in English, they have many different usages and rules, and you'll be able to choose better between them with practice.
For instance, para can also be used to talk about time, but instead of periods of time like por, you use it for deadlines. E.g. quiero el trabajo listo para el 3 de enero (I want the job done by the 3rd of January).
I'm quoting here from "A New Reference Grammar of Modern Spanish" by John Butt and Carmen Benjamin.
por and para are interchangeable in time expressions fixing the duration of some future need.
para is used to translate the idea of 'for' a specified period of time in the future:
They use some example sentences such as:
Solo queremos la habitación por/para unos días.
Tenemos agua para tres días.
Vamos a tener lluvía para rato.
For the use of por in time phrases, they say this:
Por means 'for' when referring to brief moments of time (seconds, minutes, etc.), when the speaker emphasizes the shortness of the period. The preposition may in some cases be omitted altogether.
Based on this information, I think they both could be correct depending if the sentence is referring to a future in the past or not.
I would use por. Por expresses how long something takes to happen.
So the sentence would be:
. Mi primo me prestó su cámara por dos días.
The preposition por shows the following:
Motion/place: Caminan por las calles. (They walk through the streets.)
Means/manner: Lo envío por correo aéreo. (I’m sending it by air-mail.)
In exchange for/substitution: Voy a hacerlo por tí. (I’m going to do it for you.)
Duration of an action: Trabajo por una hora. (I’m working for an hour.)
Indefinite time period: Duerme por la tarde. (He sleeps in the afternoon.)
On behalf of: La firmo por Ud. (I am signing it on your behalf.)
Per: Me pagan por día. (They pay me per day.)
The preposition para shows the following:
Destination/place: Salimos para Madrid. (We are leaving for Madrid.)
Destination/person: Esto es para Ud. (This is for you.)
Purpose/goal: Nado para divertirme. (I swim to have fun.)
Use/function: Es un cepillo para el pelo. (It’s a hair brush.)
Comparisons: Para su edad, lee bien. (For her age, she reads well.)
Opinion: Para mí es demasiado crudo. (For me it’s too rare.)
An example of por:
Te doy 20 euros por el collar (I'll give you 20 euros for the necklace.)
An example of para:
Necesito la presentación para el viernes. (I need the presentation by/on Friday.)
It all depends on what is being implied:
Mi primo me prestó su cámara por dos días. (amount of time → por)
Mi primo me prestó su cámara para (que la usara durante) dos días. (purpose → para)
Before you can choose between por and para you need to know what aisle of the Spanish supermarket you're on.
These are the only five confusing aisles, the ones that contain both por and para:
Opinion (para) vs. Indifference (por)
If you're not in any of these five aisles (or if you are, but para doesn't fit), use por.