BofA offerred this service first in 2005, and the results have been good for the customers involved.

Finextra: Bank of America says Keep the Change customers have saved over $1bn

Who
said a little change doesn’t add up? In just a little more than two
years, Bank of America’s Keep the Change savings program has helped its
customers save more than one billion dollars in customer round-ups and
bank-matching funds, the bank announced today.

Since the program was launched, these customers have accumulated approximately $10 billion in savings, including the $1 billion in customer round-ups and bank-matching funds.