OVER $13 trillion is sitting in American bank accounts and money-market funds, earning little or no interest. If consumers were even marginally more demanding, they could earn tens of billions of dollars in extra returns. That is the premise behind MaxMyInterest, a year-old electronic service aimed at slothful but yield-hungry savers. It offers to move money from banks that want to shed deposits, and that therefore pay savers low interest, to ones in need of them, and so willing to pay more. At the same time, it makes sure that each account holds no more than $250,000, the maximum amount insured by the government, providing not just higher returns, but risk-free ones.

The average interest paid on deposits in America is a microscopic 0.09% a year, according to BankRate, a data firm. MaxMyInterest’s clients receive 0.75% to 1.05%, with a weighted average of almost 1%. That may seem small, but it amounts to $2,000 a year for every $250,000 account, and should rise considerably whenever the Federal Reserve starts to raise rates. (At a meeting this week the central bank left rates unchanged, but it is still expected to start lifting them later this year.)

So far JPMorgan Chase, Citibank, First Republic, Wells Fargo and Bank of America—all titans of American banking—are working with MaxMyInterest to shift excess cash out of the accounts of willing customers. Meanwhile, Barclays, GE Capital, American Express, Ally Financial and Capital One 360 (formerly ING Direct) have signed up to receive money. Each side of the transaction has its own incentives to take part. The recipients want more deposits to fund lending: equipment leases in GE’s case, car loans in Ally’s, and credit cards for the others.

MaxMyInterest allows them to raise money cheaply, and therefore to make more loans, without having to build a network of branches.

The incentive to co-operate for the banks relinquishing cash is more complex. They fear that a customer with more than $250,000 in his account might open a new one elsewhere, to benefit from deposit insurance. The second bank, in turn, might start offering the customer lucrative services such as wealth management. To avoid such competition, the first bank would rather steer the extra cash to less threatening internet-only outfits.

Such an approach also defuses a regulatory problem. Regulators require big banks to hold especially high amounts of liquid assets against uninsured deposits. But banks earn next to nothing on these investments, making such deposits unprofitable. In response, big banks have begun discouraging them by levying fees and the like. That annoys their best customers.

Steering such deposits through MaxMyInterest allows the banks to save money while appearing more concerned with their customers’ fortunes than their own.

The idea of getting around the cap on deposit insurance is not a new one. A firm called Promontory Interfinancial Network distributes companies’ cash in $250,000 chunks to banks throughout America, for instance. But if outfits like MaxMyInterest succeed in steering a significant amount of deposits to the specialist lenders in need of them, it could spell trouble for money-market funds in particular.

They only came into being, after all, thanks to the caps on deposit rates that applied until the 1980s.

They are not explicitly insured, and currently offer minuscule returns.

Big banks should beware, too. They may benefit at the moment, but the spread of such services will make it easier for savers to shop around for higher rates. That would squeeze banks’ margins, and perhaps even change their funding models.