E*Trade did this quite a few years back - 10 or 15, IIRC. They used to offer a "max-rate checking" account that did a quite good job of coming close to matching

E*Trade did this quite a few years back - 10 or 15, IIRC. They used to offer a "max-rate checking" account that did a quite good job of coming close to matching the top rates you could shop around for. And then they decided they wanted out of the banking business, as far as I could tell, and dropped their rates to something like 0.01%. They've now outsourced it to morgan stanley's private banking and it still gets 0.05% (about 1/12 of what you can easily get at other banks).