AllFinancialMatters lays down the math on why two-cycle billing sucks.
Companies using two-cycle billing, like the Discover credit card, calculate your average daily balance using two months.
The effect is that you can end up paying interest on a balance you already paid off; potentially disastrous for customers carrying large balances.
As ever and always, only use a credit card if you can pay it off in full every month. Adding to that, avoid the Discover card.
“It pays to Discover.” Pays who? Not you. — BEN POPKEN
How Two-Cycle Billing Works [All Financial Matters]