Still, most consumers don't check the interest rates on their savings accounts, and that can cost them. According to the FDIC, the average savings account rate is a mere 0.09 percent or even less at some of the largest retail banks. Online banks pay 10 or 20 times that.
"With inflation at 2 percent, earning anything less than that means you are losing buying power," McBride said. "Over time, the loss of buying power is just as damaging as the loss of principle."
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To make the most of your savings, snag significantly higher savings rates by switching to an online bank, McBride advised. Online banks are able to offer higher-yielding accounts because they come with fewer overhead expenses than traditional bank accounts.
The best online banks also offer perks such as no minimum balance and free ATM access. You can even link an online savings account to the checking account at your local bank to access cash when you need it.
"Keep your current banking relationship but do yourself favor and move your savings somewhere where you can earn more," McBride said.
Supplementing with a high-yield savings account could mean almost an additional $500 in annual interest for the average U.S. savings account of $25,000, according to Anand Talwar, a deposits and consumer strategy executive for Ally Bank.
"On the Money" airs on CNBC Saturdays at 5:30 a.m. ET, or check listings for air times in local markets.
Disclosure: NBCUniversal and Comcast Ventures are investors in Acorns.