Zero Balance Accounts (ZBAs) from First National Bank and Trust allow your company increased investment opportunities and reduced administrative expenses. The application process for a new bank account is fairly quick.You can usually apply online in 15 minutes or less. To close a bank account on behalf of someone who has passed away, you must have legal authority to manage the account. Some will, some won't, but every bank should accept a filed small estate affidavit. It is often necessary that the property and financial affairs of a deceased person be supervised through a court process. My dad passed away two months ago. Got the death certificate in hand and went to the bank to close his account. No, there is no minimum balance requirement with Illinois Funds accounts. You may draw your account down to a zero balance without the account being closed.