Okay, I think I see where you're coming from now. With the 2% reward from the credit card, using it today is -$980 today, and cash is -$1000 today. If you do the math to see what interest rate you'd need for paying cash to be the better option, you do indeed get an infinite APR. This matches with common sense: if your net cash flow is zero at all future times either way, you're always better off paying $980 today rather than $1000, no matter what interest rates are.