Rates have soared for mortgages, credit cards, auto loans, and a range of other debt products, but not for savings accounts at big banks used by millions. 

Yields on savings accounts at megabanks such as Bank of America and Chase remain near zero. Savers, many of whom might lack financial discipline after years of living in a low-rate environment, have trillions in accounts that are yielding nothing and getting eroded by inflation.