I’m chasing American Express (AXP) as an aspirational brand. I don’t think it can speak to millennials and say, “Trust us. We’re looking after your financial interest.” I don’t think its prestige works for the young. There’s an opportunity to create an equivalent brand—but “prestige” isn’t the right term. They care about transparency, usability.

On why he started his firm

As people graduate from college, they may have to put a deposit down on an apartment. They’ll need a car or a real bed. These are all credit decisions. People ages 18 to 34 are predisposed to hate banks. They want financing, but hate paying interest—hate the idea of being stuck in debt. But they’re willing to pay a fee upfront to split a payment over several months. We can underwrite people that the system sees as terrible risks with better clarity.

On PayPal’s unfinished business

At PayPal, the plan was to build “the new world currency.” We never got there. Payment innovations always start with a lofty view of digital money but dead-end at “the rails”— issuing banks, acquiring banks, etc. Affirm is an attempt to build a bank the way it should be done in the 21st century.

On his return to fin tech

Building financial technology is hard. Really hard. Startups are always hard, but fin tech is a whole different level of self-inflicted pain. You’ll be regulated. You’ll deal with big banks. They’ll see you as little and cute until you’re meaningful. Once that happens, they’ll want to crush you out of existence.

This story is from the April 1, 2015 issue of Fortune.