Banks in the U.S. are still leery of issuing loans to local small businesses, but one nonprofit says it has figured out a way of getting a 90% repayment rate on business loans to the types of people no financial institution would trust--young people in poor African countries without as much as a permanent address.

"You are sending hundreds of dollars to low-income 22-years-olds living in shacks in the slums of Nairobi. It sounds like a scam," said Julia Kurnia, founder and director of Zidisha, a nonprofit that hosts...