Savers, here's what it's come to: Barclays is bragging that its 1 percent interest on an online savings account is 12 times the U.S. average. Ugh. Yes, that offer really is among the highest you'll find on a savings account in a search on bankrate.com. But it's now topped by an offer that just came out from a just-launched, savings-only division of San Francisco-based MUFG Union Bank. The new entity, PurePoint Financial, offers a rate of 1.25 percent on a savings deposit of at least $10,000, and 1.4 percent on a $10,000, 12-month certificate of deposit.

If those rates still don't seem like much to celebrate, a little perspective might make them more attractive: The main lending unit of MUFG Union Bank's parent, Tokyo-based financial services giant Mitsubishi UFJ Financial Group, pays retail savers in its home country a barely discernible rate of 0.01 on fixed-term deposits of up to 10 years.All that PurePoint Financial offers, as a "hybrid digital bank," are no-fee, FDIC-insured savings accounts and CDs. Its president, Pierre Habis, says it will have "consistent top-of-the-market" interest rates, not just teaser rates for a limited period. There are no checking accounts, debit cards, or networks of ATMs.

There are, however, a handful of brick-and-mortar offices PurePoint calls "financial centers." A company press release says the centers offer a "modern, streamlined, cashless experience." A handful of the spaces have opened in Dallas, Tampa, and South Florida, and more will open in Chicago, New York, and Houston later this year. Those offices—23 locations have been leased so far in those markets—will be staffed with people Habis says can walk consumers through the ins and outs of savings, including using an FDIC insurance calculator. PurePoint says its research shows that serious savers don't want their money to be accessible. Rather, Habis said, "consumers want honesty, simplicity, transparency and they do not want to be cross-sold products."

In a press release it put out on Thursday, PurePoint said that it "pledges to help grow America's personal savings rate."

It will also serve another purpose—to help MUFG Union become become among the U.S's top 10 deposit-taking banks. Right now, it's No. 21, ranked by total deposits.

A potential challenge for ventures that go after rate-sensitive deposits is whether they can keep those deposits when more rate competition shows up. That may be why PurePoint is emphasizing that it has brick-and-mortar centers, too.

"By having a physical location, you build more of a brand and feel more emotionally connected to a company than if a bank is only digital," said Alan McIntyre, senior managing director of global banking at Accenture. "If a business is purely for deposit-gathering, you don't need to brand it or do much with it. If you're at the top of the rate list, you'll get the hot money."Right now, Americans' savings rate, at just 5.4 percent, could use some help. If interest rates rise, there will be a little more variation in what banks can offer consumers, and you'll see more competition around buying consumer deposits, noted McIntyre.

That would be a welcome change.—with assistance from Gareth Allan in Tokyo

This article was provided by Bloomberg News.