Cost of living / Cheap apartments in South America.

In general depending on location apartments are cheap in Peru, Chile and Argentina and rooms even cheaper.  You can use Locanto to look at ads for rentals in the larger South American cities.

For Instance, for Lima, Perú, see this link:
https://lima.locanto.com.pe/

Then under INMOBILIARIA (or INMUEBLES in Chile) click on the first line, Departamentos en alquiler to see apartments for rent.  The second line is rooms for rent, Alquiler de habitaciones (or Piezas en arriendo in Chile).  Rooms in South American cities are quite cheap and often they may come with meals and laundry, or those services and others can be negotiated.

The ads on Locanto are posted for free, so many owners will post there but also agencies.

For Santiago, Chile look here:
https://santiago.locanto.cl/

For the larger cities in each country you can just do a search, for instance:
locanto concepcion
...will get you Locanto for Concepción, Chile:
https://concepcion.locanto.cl/