There are several banks to choose from in the VI.
First Bank, Bank of the VI, Scotia Bank (Canadien) and Banco Popular (Latin American)
I only know about First Bank, Bank of VI (US Banks protected by FDIC) and Scotia Bank.
When opening an account, they require 2 forms of picture Gov't issued ID. (drivers lic, passport, etc.)
If depositing money to open the accounts, they require proof of where the money came from: (other bank accts, wages from work, etc)
Checking/Savings accts are opened the same day, but if checks are deposited on that day, you have to wait for the checks to clear before you're allowed to withdraw. Here in the VI, out-of-country checks can take 10 days to clear.
Loans are made based on your residence status, salaries, ability to repay the loan and credit history.
Any of the banks here are very good banks. One not better than the other.
