“Maybe interest rates are too abstract for people to really appreciate what the differences mean,” Barrington says. “Convert the extra amount you could earn to dollars when you compare banks, and you'll probably see that extra is worth having.”

For those not ready to test the waters of online-only banking, the survey also revealed that medium-sized banks - those with between $5 billion and $10 billion in deposits - offered an average savings account rate of 0.277 percent. That was more than 10 basis points higher than their smaller and larger counterparts - albeit roughly half the yield of what the typical online-only account offers.

Desperately seeking safety

Admittedly, no interest rate of less than 1 percent is likely to raise investors' pulses today, particularly in light of the gains the stock market has posted lately. Yet for some consumers - including many retirees - an FDIC-insured bank account may be the wisest place to store savings they would rather not risk in the stock market.

“Money on deposit should be your safety blanket, the totally secure area of your investments,” Barrington says. “Even so, there is no reason to make sure that money isn't working as hard for you as it could be.”

The MoneyRates.com survey offers more details on the top banks in the survey and its methodology.  

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