The post may be updated if more banks join the list :D
below are some banks in which IMGs can open an account without having a Green Card:
Bank of America:
Pros:
1- Available nearly everywhere
2- It gives you a temporary card that you can use for 30 days until your permanent card arrives
3- It has a nice mobile app (better than other banks in my opinion) that can basically do anything, easier than calling them or going to the bank.
Cons:
1- To avoid the monthly fee of 12 dollars, you have to maintain your balance above 1500$ at any point during the month or you have to deposit 250$ per month.
2- For IMGs, they require 2 forms of identification (compared to one in most of the other banks). These 2 can be your passport and international driving license.
3- If you wanna travel outside the US, it is preferable to activate the “travel notice” feature (via visiting the bank or the app or calling them) because they may temporarily block your debit card if you are using it from a different country.
Don’t forget to go paperless (either using your mobile app or by asking them in the bank) to avoid having infinite unnecessary papers mailed to you especially if you are staying temporarily at a friend’s place!
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Citizens Bank:
Pros:
1- They require 1 form of identification.
2- To avoid their monthly fee of 10$, you can either deposit or let any friend deposit in your account each month even if a dollar OR simply you can open another account for free and auto-circulate a dollar monthly between the 2 accounts and voila, no fees at all.
Cons:
1- They are less available in some states like Ohio and NY where you will find ATMs only and hardly any branches.
2- They don’t give you a temporary card when you open your account, so you should leave some cash with you till the debit card arrives.
3- YOU HAVE TO TELL THEM YOU WANNA GO PAPERLESS, or else they ll charge you 2 dollars monthly for bank statements that are mailed to your physical mailing address.
When you call Citizens Bank and it asks you for a Social Security Number (SSN) to let you talk to an employee, just wait and say nothing. You ll be asked about the SSN 3 times then you ll be auto-transferred to a human employee.
Good banking everyone :D and don’t forget to comment if you know more "IMG-friendly banks"
And that’s it
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Update 4/8/2018
Some friends mentioned: CHASE and Wells Fargo so you may try them too
(Wells Fargo pros and cons are very similar to Bank of America)
-Murad