Silicon Valley has helped enhance just about every aspect of modern life. Naturally, Mohammad Mansour figured it could help solve his money problems, too.

Mr. Mansour borrowed $7,680 from Lending Club, a San Francisco lender offering loans more conveniently and with lower interest rates than a traditional bank. He then obtained a $10,000 loan from Prosper, another online lender based in Northern California.

An accountant from Queens, Mr. Mansour earns about $64,300 a year. He took out a third online loan and then a fourth. He now owes $31,600 to three virtual lenders. And he is struggling to pay off the debts.

He is one of more than a million Americans who have tasted what many believe is the future of finance, in which big, lumbering banks with outdated branches and skittish risk departments are being replaced by lenders that operate mostly online and match borrowers with investors who buy up large chunks of the loans. Using the latest data and credit algorithms, the lenders can approve loans in a matter of minutes.