STOCKHOLM — Ready to check out online? Just enter your email address and a postal code to complete the purchase. The bill will be in the mail.

That is the simple option offered to shoppers on 45,000 e-commerce sites using Klarna, a fast-growing online payments service start-up run from a newly refurbished downtown office here.

Enter a few bits of information and your online shopping generates a flurry of activity at the company. In seconds, Klarna analyzes reams of credit sources and online purchasing data to determine whether it will assume the liability for your purchase.

If you are a returning Klarna user, buying during regular working hours or shipping to your usual address, an email and postal code are probably enough. Klarna may even let you pay for the goods up to two weeks after they have arrived in the mail.