I actually went to the AFP Prima office. If you want to take out your funds, there is a whole lot of red tape you have to go through. First, you have to get a job in the US that has a pension plan. Then, you have to submit documents, which have to be translated and appropriately sealed, so that they can transfer the funds to that pension plan. You also have to renounce your residency and show them that letter. I went to the immigration office here in Pucallpa, and I was told that you have to pay around S/.40 to do that. Once you make the payment and get the letter, you have 15 days to get out of the country.
AFP will transfer your money to a bank account ONLY IF the country where you are residing doesn't have a pension plan.
The AFP Prima rep I talked to told me that it would be easier to just wait until I'm 50 years old, which I'll be in about 8 years. There's a law right now that says that a woman can withdraw most of the funds if you have not contributed for a year or so. I asked her if not having my carnet de extranjeria number would be a problem, and she told me that all I have to do is update my information with my passport number. Then, when the time comes I can do the necessary paperwork to withdraw the money. I can't imagine it being as simple as I was told, but I'll cross that bridge when I get to it.