Well hopefully there won’t need to be an American version of Monzo because Monzo will be able to expand to America
I’ve summarized what we know about Monzo’s ambitions, preparation for entering new markets & some of the challengers that ‘challenger banks’ currently face in the US, in this post -
https://community.monzo.com/t/newspaper-financial-technology-start-ups-to-get-a-license-to-bank-in-the-usa-the-new-york-times/6851
which also includes a link to some changes to regulations that should make it easier for Monzo to set itself up as a bank in the US.
It also helps that Monzo’s focus is on developing a current account only while offering user’s access to other service providers (for credit cards, mortgages, savings accounts etc.) so fewer regulations would apply to Monzo.
But that doesn’t mean it’ll be easy - as recently as 2011 no new banks were set up in the states & the number that were created each year had been trending downwards before then.
Monzo might not try to set itself up as a bank in the US, if it expands there at all, of course & in which case, it could offer a prepaid solution like the one we currently use in the UK, while we’re waiting for the full banking license.
A couple of days ago, it was announced that customers will be able to apply for prepaid cards which offer overdrafts which may support Monzo’s business model (it plans to make at least some of it’s revenue from it’s first product which will be overdrafts)
http://www.usatoday.com/story/money/personalfinance/2016/12/04/overdraft-coming-prepaid-cards-heavy-restrictions/94763686/
There are a number of companies like Monzo in America already:
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Moven (as Ian mentioned) who have an interesting looking feature that sends alerts when your spend is higher than normal
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Simple who have a savings goals feature that appears to be well designed
And a lot of other prepaid card providers but it’s difficult to find others who’ve taken Monzo’s user experience (as opposed to financial product) first approach.