Late last year, just in time for Christmas shopping, Rachel Rhoads got a nice surprise. One of her secret savings accounts had grown to $900 behind her back.

Rhoads, a 37-year-old Los Angeles-based sales director for a jewellery line, has an account with Digit, a financial technology company with an algorithm that tracks users’ income and spending patterns. It painlessly spirits small amounts of money out of checking and into a savings account every two or three days.

“I just thought it was such a good idea, to set it and forget it,” said Rhoads, who says she is “like a squirrel” in her approach to saving. Digit sends texts with balance updates, which she largely ignores because “I like to pretend the saving is not happening”.

Getting consumers comfortable with putting their finances on customised autopilot, starting with a simple, no-fee-and no-interest savings account, is the San Francisco start-up’s mission. In two years, its users have saved more than $250 million this way, according to its 31-year-old founder and chief executive officer, Ethan Bloch.

When the product moved out of pilot mode, in February 2015, users were saving $4 million a month; now that’s $30 million a month. Digit won’t disclose the size of its user base but says it has tripled from about a year ago.

Digit had a savings bot before bots were cool, or at least before the hype in the financial technology world reached a fever pitch. Its product is simple. An algorithm looks at a user’s average, high, and low checking account balance, when the user is paid, and whether the pay cycle is smooth or choppy. Then, after looking for bills due in the next week or two and analysing recent spending, it moves an amount it judges the customer won’t miss to a savings account. The company makes money from the interest rate it gets on account assets.

Digit has announced that it will be the first savings bot on Facebook Messenger’s platform, so users can just use Facebook to communicate with it. When Digit moved out of its pilot phase, it communicated only by text, a natural language for many users, since 17 per cent of them are aged 21 to 24, and 44 per cent are from 25 to 34 years old. Rhoads said they’re “cute texts” with “some personality” and “not annoying at all.” After text messaging came iOS and Android apps for users.

The company is now working on what Bloch called “the first artificial intelligence-powered financial goal programme”. Users would set a date and amount (and pick an emoji, of course), and Digit’s algorithm would make a series of projections based on balances to determine the optimal amount needed to start saving towards that goal — or point out that the goal is unrealistic.

Also on the product horizon is having Digit’s algorithm figure out how to “move every dollar where it should go, at the right time, to minimise fees [on student loans, credit card accounts, etc] and maximise gain,” Bloch said.

There are hitches. Since Digit isn’t a bank, it can’t pay interest, and it will be competing in an environment of rising rates. Bloch said interest rates “are not a huge deal” for his customers, because they regularly withdraw money and tend to save small sums.

Another hurdle is that traditional bank technology can make it hard to connect accounts. “Banks have not made it easy for customers to get their data,” Bloch said. “Because of that, Digit and products like Acorns, Venmo, Betterment — every day we have bank difficulties that affect thousands of customers.”

Behavioural finance underlies much of Digit’s design. Take the goal function, for example: if users get more specific about what they are saving for, research suggests, they are less likely to withdraw the money.

“If an account is labelled ‘Charlie’s Education Fund’, I’ll think harder about withdrawing it than if it’s just labelled ‘Savings’,” Bloch said. Currently, 70 per cent of Digit users withdraw 80 per cent of their savings every 90 days, mainly to pay bills and meet short-term needs for cash, to pay off debt, or pay for travel.

“Digit is an easy, elegant product,” said Ryan Falvey, a managing director at the Financial Solutions Lab at the Centre for Financial Services Innovation. In 2015, the lab, part of a non-profit group that supports entrepreneurs looking to use technology to improve Americans’ financial health, launched a competition to “identify solutions that help households better manage their finances on a tight budget”. Digit was one of nine winners, out of about 300 applicants, to get $250,000 and other resources to help develop their products or services.

Other winners included Even, which uses technology to create smoother income streams for workers with uneven cash flow, child support app SupportPay, and low-rate lender Ascend Consumer Finance.

Bloch’s broadest long-term goal is to make Digit’s user interface far more conversational, to “humanise it” so users feel more in control when they communicate with it.

“We want to make Digit understand more — not as broad as Alexa or Siri, but widen the aperture a little more — related to finances and your money,” he said. “One day, it would be awesome to say, ‘Hey, Digit, am I OK for retirement?’ And all Digit does is send back a thumbs-up emoji.”

That kind of complex analysis won’t show up anytime soon. But after a Series B round of fundraising led by venture capital firm Ribbit Capital, Digit’s 22-person team is sitting on $25 million in cash. That, Bloch said, will let the company “be somewhat protected for the next few years in pushing the envelope, largely to invest in product development. The big question for us now is, what more will our customers trust Digit to do?”