This is not necessarily applicable to the entire country but it definitely is the case here in Da Nang. I have talked to people about this a great deal over the years and I now know the true answer because it was true for me, and I recently accomplished it.
If people are trying to spend any real length of time in this country, eventually you are going to need or want a bank account. For a while, I, just like most other people was obtaining cash by using ATM machines or some other method and then I was paying fees that banks rip us off with to allow us the pleasure of accessing our own money. Vietnam is also notorious for having really low withdrawal limits on the machines so for someone that is trying to do something like pay their rent, this can mean needing to use the same machine many times in a row and of course, the machine charges you a fee for each use of the machine.
Once someone has lived here for a while it just makes sense to get a Vietnamese bank account and then it is much cheaper to get money into the country, certainly a lot more than using ATM's and paying foreign transaction fees as well as whatever rate they are offering on the exchange which in many cases, is not a very good rate and they are not even required to tell you what the rate is when it is transitioning it from USD or whatever to Vietnamese VND.
It really isn't that difficult to set up a Vietnamese bank account but the hurdles you are going to face is that the people behind the counters at the bank as well as the other staff that are working there either don't know the rules or they are making up rules because they don't want to go through the hassle of opening a new account.
Many people end up getting told by the staff at a bank that it is illegal for foreigners to have Vietnamese bank accounts and this simply isn't true. I don't know why the banks are doing this but it could just boil down to pure laziness. So here is what you have to do in order to get a bank account in Da Nang and while it might take an hour or so and involve using a translating app, you can get it done and it costs very little if anything at all.
First off you need to locate one of the major branches of whatever bank you want to have an account with. It doesn't really matter since all of the major banks have ATM machines everywhere so just choose one at random. The easiest ones in my experience has been CIMB or even better Sacombank.
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Then you need to locate a major branch for these banks and this can be a bit tricky because it is not like the main branch is labeled as such on the building or online. A good rule of thumb is to head to this particular part of town as it is considered the "financial district" of the city.
You can see the Sacombank on the map there but all the other banks have their locations here as well. This is the area that is just north of the very identifiable Dragon Bridge so just head over there. A point of reference that most foreigners will know here is the rather famous bar Bamboo 2, which is just a few blocks away from the banks.
Bring your passport with you and just tell the security guard or helper at the door "new account" or better yet, have these two words loaded up on a translation app when you arrive. You might still get some staff member that tells you that you are not allowed to open a bank account on a tourist visa or something else like that. I wouldn't argue with them too much even though they are incorrect about this. It is completely legal for a bank to open an account for literally anyone. However, they are not legally obligated to do so either. So if you run into a gatekeeper that is giving you a hassle, I would recommend that you say something like "are you sure? Friends of mine have banks here" even if that isn't true. Hell, if they are going to lie to you, you may as well throw it back.
If they still insist you cannot have an account simply move on to the next bank. Seriously, there are like 20 of them in this one small part of town.
You are going to be signing a bunch of documents that are not in English but this is nothing to worry about. After all, it is completely up to you how much money you put in this account. If you are American you will have to fill out some US tax form as well and initially this kind of scared me off but the bank and my agent informed me that it is just policy, that document will never be submitted to the United States and this begs the question "why bother then?" I will admit that I "accidentally" messed up my Social Security number on the form to test to see if that would create a problem and it didn't. I suspect this form simply goes into some file somewhere that nobody ever looks at.
When they open your account you will get your card the next day and honestly, it makes life a lot easier. Do not believe people both foreign and Vietnamese that tell you that you cannot open a bank account here if you are a foreigner, it simply isn't true. I should know, I have 2 bank accounts now and have had no issues. You just have to be a bit smart and persistent.