Normally, when I want insurance coverage (e.g. for my car and house), I have to pay a premium to the insurer. My bank account comes with deposit insurance to insure me against bank collapse. It looks like I do not have to pay any premium for the insurance coverage. Is that the case? If so, who is paying the insurance premium?
If you are asking who sends the insurance payment to the (presumably) government insurer, the bank does. You'll never see a "deposit insurance" fee.
In economics, however, there is the concept of "incidence" which seeks to determine who actually pays a fee or a tax. In practice, for example, the incidence of payroll taxes paid by the employer fall almost completely on the employee in the form of lower salaries. Similarly, in practice, it is customers that ultimately pay the cost of deposit insurance in the form of lower rates and various fees.
That said, deposit insurance is rather inexpensive. In the US, for example, banks pay between 1.5 and 40 cents per $100.00 of deposits with most deposits tending to the low end of that range. If you have, say, $10,000 in a bank savings account, that means that the bank is paying between $1.50 and $40 a year for deposit insurance on your balance. If you're at a large, well established bank, they're probably paying much closer to $1.50 than $40 a year.
In all cases the customers pay the insurance, they just don't see it on the monthly statement. If you are a member of a US credit union it is possible you might see a line in their annual report. If you are looking at the investor reports for a banking company you might see it listed in the filed financial statements.
The interest the bank charges for loans is to cover all their expenses, everything left is profits. The expenses include: interest paid on deposits, employee salaries and benefits, amount lost to bad debts, equipment costs, rent, electricity, and government fees. Those fees include deposit insurance.
Whenever you have ask who pays. It is always the customers. The company should hopefully be able to set their prices to cover all their expenses, and thus be profitable.
The FDIC receives no Congressional appropriations - it is funded by premiums that banks and thrift institutions pay for deposit insurance coverage and from earnings on investments in U.S. Treasury securities. The FDIC insures trillions of dollars of deposits in U.S. banks and thrifts - deposits in virtually every bank and thrift in the country.
Remember when you opened the account, and you didn't get a free toaster? (that used to be a thing, years ago: getting free stuff like that when opening a bank account).
Or they paid you a signing bonus to open the account, but it was only $100 not $125?
Or the monthly fee was not $8.50 but instead was $9?
That is you paying for deposit insurance. That money paid that money to FDIC or FSLIC instead of passing it on to you.
I have no idea what FDIC does with all those toasters :)