Want a better savings account? Here's why you should break up with your bank today

For nearly a decade now, the average savings account has been paying off next-to-nothing, thanks to the central bank — the Federal Reserve — maintaining a policy of keeping interest rates near zero to spur borrowing. The national average savings account rate has been stuck at 0.06% since mid-2014, according to the FDIC, while money market account rates have held at 0.08% since 2014.

But now that the Fed has raised rates twice in the last six months — and is expected to do so again later this year — certain banks, especially online ones, are jumping on the chance to offer more competitive yields in hopes of attracting more customers. "We've seen continual improvement," said Bankrate's Greg McBride in a phone interview.

Still, giant brick-and-mortar banks like Bank of America continue to pay you peanuts yet attract tons of customers. Blame inertia and convenience — or at least the perception of it: The truth is that more and more online banks reimburse ATM fees, so you don't need a bank with lots of locations.

Are you sick of losing out on interest, which is essentially free money? Bankrate's data suggest it really pays to shop around: Two examples of accounts that pay decently on savings, with essentially no minimum deposit requirements (just $1), are at BankPurely and DollarSavingsDirect.

BankPurely, an online bank aimed at millennials, is offering 1.3% yields on savings deposit. DollarSavingsDirect, a digital product of New York-based Emigrant Bank, also offers 1.3%. By way of comparison, Bank of America is currently offering just 0.03% on savings accounts, while Citibank is offering 0.04%. (You can check out the full, location-based Bankrate data here.) 

The recent jump in interest rates can be seen when compared with what the top yields were in October, before the Fed hiked rates. And, as Mic recently noted, it has become increasingly common for the very best specialty checking accounts to pay even higher interest than the best savings accounts — even if savings and money market accounts pay more on average.

For example, the Northpointe Bank UltimateAccount actually pays a rate of 5%, though it comes with certain qualifications, like a minimum number of debit card purchases per month.

McBride said online banks are offering higher rates mainly as a way to compete against traditional banks: "They don’t have branches on every corner," he said. "They don’t have their name on the stadium, so how do they outmarket and outcompete the banks that do? Offer a better return."

Though they're not as widely used, certificate of deposit or CD accounts at online banks are also seeing similar yield increases, McBride said. CDs require that you keep a minimum amount of money in the account for a fixed term; if you pull out your cash early, you pay a fee.

The rates on offer for these products are up to a full percentage-point higher than the highest savings rates on offer. You can check out that list here; one example is Ally, which pays 2.25% if you are willing to keep your money in the account for five years.

Whether keeping your money locked up for so long is smart? That's another question — since rates might continue to rise and you might end up regretting that commitment. With a checking or savings account, you can withdraw your cash without a penalty whenever you want.

Sign up for The Payoff — your weekly crash course on how to live your best financial life. Additionally, for all your burning money questions, check out Mic's credit, savings, career, investing and health care hubs for more information — that pays off.