Fluctuations in the Fed Funds rate do not explain why this bank is offering 0.1% on a savings account. The Fed Funds rate explains why ING and is offering 3.x% instead of 4.x% (for example), but 0.1% is so small a rate that I think something else is going on. I think it’s actually tied to the previous bubble: the Internet.
The rise of internet banks and high-rate savings accounts changed how best to compete for customers. Traditional banks are competing with things like customer service and convenience, and for the most part ignoring interest rates, where they can’t compete. Your bank is offering such a low interest rate because it has determined that a higher interest rate on savings accounts is not worth it in terms of keeping customers, because any customers they have who are very interest-rate sensitive have already gone to the big internet banks.
Now, your bank, which I’m guessing is a traditional brick and mortar business, can’t compete with the likes of ING. Their overhead is simply too high. And general half-measures won’t get them there. If ING is paying 3% and Bank X brings their rate to $1.5%, they still lose all the customers who are very interest-rate sensitive, and they end up having to pay out extra interest to the many customers who just don’t care. Now, maybe they could offer 2.75%, which might make the gap enough to keep interest-rate sensitive customers from switching, but (1) it won’t lure back the ones that have already switched and (2) it will be even more expensive than the 1.5% option. So, there end up being two stable and profitable interest rate regions for banks to occupy. They can either pay very close to the best market rates, hoping that the gap will not be large enough for anyone who cares to jump ship, or they can pay a pittance, knowing that everyone who cares about interest rates is going to leave anyway, and they cut their costs. Presumably they don’t pay 0.00001% because it’s embarrassing.
Now, they do make some accommodation in the form of a higher rate for large balances. This is because as the balance gets bigger, so does interest rate sensitivity. So the bank has to increase their payout to keep the cost to their larger customers of switching lower than the benefits. If they offer other improved services to large account holders, this might make sense.