The median American household has a combined balance of $10,000 in its checking and savings accounts, according to a census estimate. For the last few years, anyone keeping this amount in a high-yield savings account has earned close to 4 percent annual interest, or about $400 a year.

But the average savings account interest rate is closer to 0.4 percent. And the nation’s three largest banks — Bank of America, Chase and Wells Fargo — offer 0.01 percent on their standard savings accounts. That works out to $1 in interest a year for a $10,000 deposit.

Banks make up for those dismal rates with perks like numerous branches and A.T.M.s, but they also know many of their customers won’t hunt for better deals out of inertia.

The Consumer Financial Protection Bureau said one bank, Capital One, went too far by intentionally creating confusion so that customers wouldn’t know to switch to a higher-paying account at the same bank. Here is the difference in what they would have earned in interest:

The consumer bureau sued Capital One in mid-January, arguing that the bank misled customers by creating a new high-yield account called 360 Performance Savings, while letting an existing account, 360 Savings, languish at a lower interest rate. The bank had earlier advertised that account as having “one of the nation’s highest savings rates.”

The agency estimated that Capital One avoided paying $2 billion by not automatically converting each 360 Savings account to a 360 Performance Savings account.