But Digit could lose a chunk of its user base after it announced last week that it will start charging $2.99 a month for the service, after a 100-day grace period.

The news sparked an immediate response from angry users who said they would be closing their accounts. “Loved digit, hate the ideas of fees,” one person commented on the company’s Facebook page. “Makes no sense to pay to save,” wrote another.

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Digit’s chief executive Ethan Bloch called the fee a “transparent” way for Digit to make money that would give the company more room to develop other services. Bloch told The Post he didn’t want to resort to selling customers’ data or partnering with companies that may want to sell financial products to Digit’s customers. “On Digit’s side, we can be beholden to nobody but our customer,” Bloch says.

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As part of the change, Digit is also increasing the annual “bonus” it pays customers to 1 percent of the account balance, up from 0.2 percent. That means that customers would need to have at least $3,600 in their accounts to break even on the $36 annual fee.

Rival savings apps that aren’t (yet) charging fees seized on Digit’s announcement to try to win over users. For example, the savings app Qapital, which lets users create rules for when savings should be automatically deducted, says it saw a record number of app downloads the day Digit announced the fee. The app is offering $10 bonuses to new customers who open and fund accounts in April. Chime, a mobile banking app that offers free automatic saving for every time customers use their debit cards or every time they are paid, says account openings have increased by 20 percent since last week.

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But Digit is betting that some people who feel they may never get around to saving otherwise will be willing to pay a few bucks a month to have the app save for them.

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Some studies show that consumers often drag their feet when it comes to making major financial decisions, such as opening a savings account, even when there is a financial incentive for doing so. Human nature tends to hold back many consumers from making savvier financial choices, says David Blanchett, head of retirement research for Morningstar, a fund research firm. “Whatever is the easiest path, people tend to go with it,” he says.

Digit is not rolling out any new services now, but down the line, Bloch says he would like to go beyond saving to help people figure out how to pay off their debt more quickly.

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In the meantime, users will have a decision to make. “They can decide ‘is this worth it?’ And if not, they don’t have to use it,” Bloch said. “If they think it is worth it, then they know exactly how they’re paying for it.”