Risk-free interest? In a bank? Are you kidding?
If you pick a large bank, your deposit is within the limit for federal insurance, I guess you could say it is risk-free.

Who insures the insurer?
The insurer is the FDIC and the FDIC is backed by the US government who can essentially print near unlimited amounts of money without causing massive inflation. The FDIC also can raise premiums that they charge banks for insuring the deposits.
So, if the FDIC runs out of money (because of multiple bank-runs), the U.S. government will print as much money as necessary to cover the FDIC deficit, thus making the taxpayers pay all the debts.
How do you figure taxpayers pay?
How dare you ask me questions now having not answered my own?

But never mind, I know that you can't answer anything coherent, so it doesn't matter. Regarding the taxpayers money, it is called socialization of debts, when ordinary people ("taxpayers") would indirectly pay for the bank debts by lowering their standard of living through inflation since the government would print money to cover the debts (this is called seigniorage, i.e. "a right of the lord (seigneur) to mint money" from French).
What does this have w FDIC running out of money? FDIC has $500B line of credit @ Treasury.
Are you talking about QE "printing money"? Please show inflation if thats what you claim.
No, that was not my claim, you just see what your eyes want to see. I was not talking about QE "printing money". There is no inflation out of this, since the QE money doesn't leak into circulation. I was talking about how debts are socialized and the burden of them is passed on to the taxpayer in general (by means of inflation).
Is this your original claim? that if FDIC needs money. Fed prints money. Inflation follows. Taxpayers "pay the debt" of the FDIC via "debt socialization"
You might have noticed (well, you actually didn't) that I was talking about how socialization of debts works, and I specifically mentioned "in general". Regarding the FDIC, I don't know how much money they might potentially need, but if you insist, the answer is affirmative. In the worst case scenario, the sequence you described would necessarily lead to inflation (since the money "lost in debt" didn't disappear but just changed hands).
In the event that the FDIC fund is insufficient, the FDIC has credit at the Treasury. The Fed isn't even in the picture. Theres no protocol so an act of Congress is probably required to do what you are suggesting
Even if the Fed lends them money, then the borrower (FDIC) pays back the loan not taxpayers.
Please prove the concept of "socialized debt" w real world evidence