I have some credit problems now. I cannot get any banks to allow me to open up a savings account. I do not want a checking account. Are there any banks out there that will allow this?
Yes, there are, they don't advertise that fact because they don't want to attract problem accounts. In general, banks are more likely to open a savings account than a checking account when the bank sees credit problems in the customer's history.
Keep trying. You may have more success if you are able to apply for an account on a bank's online system rather than in person. That doesn't make a lot of sense from a bank security perspective, but it's been done. You may be at a disadvantage if you are in a small town with few banks.
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