America's four largest banks -- Chase, Bank of America, Wells Fargo, and Citibank -- have almost $9.5 trillion in total assets. If these four banks formed their own country, they would have the third-largest economy in the world behind China ($17 trillion) and the U.S ($25 trillion).

Let that sink in for a second, then consider this. With the exception of Citibank, the other three offer the lowest annual percentage yields (APYs) on their savings accounts. In a number, each one will pay 0.01% on your savings. Of course, these banks also have big overhead costs to cover, but it's still amazing they can't offer at least 0.02% on your money.

So what does it take to earn more than 0.01% for your hard-earned cash? How about opening one of the best high-yield savings accounts available today -- the CIT Platinum Savings. This account offers one of the best savings rates, plus a few other perks that give it a leg up on its competitors. If savings accounts at big banks don't interest you, here are some reasons to consider the CIT Platinum Savings.

1. Competitive APY

The CIT Platinum Savings earns a competitive 4.70% APY on balances of $5,000 or more. Note that you'll need to maintain a minimum balance of $5,000 to snag this amazing rate. If your balance drops below that threshold, your APY will fall to 0.25%. The upper part of this APY tier, however, makes the CIT Platinum Savings one of the best high-yield savings accounts out there.

2. No monthly fees

The CIT Platinum Savings has no monthly service fee. This differs sharply from the savings accounts at larger institutions, which often have them. Additionally, this free savings account has a low $100 minimum opening deposit, though, again, you'll likely want to plan to deposit at least $5,000 so you can snag the higher APY.

3. Links to a CIT eChecking account

One common problem with online-only savings accounts is cash access. Many online banks have limited options for withdrawing cash. For many savers, this creates a dilemma. Either you can limit access to your money and score a higher APY, or go with a big national bank and access money whenever you need to. With the top four banks in the U.S. having a total of $9.5 trillion in assets, it's safe to say that most people go with the latter.

While CIT Bank doesn't have brick-and-mortar branches, it does offer ATM access through its eChecking account. Like the CIT Platinum Savings, the eChecking account has no monthly fees and earns a little interest on your balance. It comes with a debit card, which you can use to withdraw cash at ATMs.

Better yet, CIT Bank reimburses you up to $30 in ATM fees every statement period. Very few banks will reimburse you for ATM fees on basic bank accounts, making this an incredible deal for a free checking account.

You can open both a savings and checking account at CIT Bank, then link them together. When you need to access money from your savings, you can then transfer it to your checking account and use your debit card to withdraw it from ATMs. This will take much less time than transferring the money to an external account, which could take a few business days to transact.

CIT Bank isn't one of the four largest banks, but it's super safe

Finally, it's important to note that CIT Bank is a safe place to store your money. While its total assets aren't in the trillions, it has more than $200 billion, making it one of the 20 largest banks in the U.S. And it's a member of the FDIC, meaning your cash is protected (up to $250,000) in the event of bank failure.

Of course, if you'd rather have in-person banking support or the security of knowing you can withdraw money at a bank branch close by, CIT Bank is likely not for you. But for high APYs and no monthly fees, few banks will offer you a better place to store $5,000 or more in savings. Compare it with some of our other favorite banks and see if it has the right services to meet your banking needs.