Bottom line is you need to spend $500 (if DVC or AP) in order to pay itself off. I don't see where you have added your 20% off in your calculations. You have taken off $100 though?!? The $100 should be added to your total, it's the added cost of purchasing the card. Then you take 20% off every bill you get. That's where the $500 comes in. Savings will cover the card purchase after $500 spent. So according to your total, you will save 20% off your $150 (650-500) or $30. That's your savings after recouping the $100 spent on the card. From this point on, you are saving money every time you use your card. Hope that helps and doesn't confuse you more! ETA - check out the breakdown of savings in post #3 of this thread!