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If you want to have credit card with great rewards, you may choose the Discover it® Cash Back credit card. This card comes with 5% cash back on everyday purchases at different places each quarter like grocery stores, restaurants, gas stations, select rideshares and online shopping, up to the quarterly maximum when you activate, all other purchases will earn 1% cash back. What is more, Discover will match ALL the cash back earned at the end of your first year (if you are a new cardmember).
When your credit is bad, you most likely won't find a credit card with rewards. However, earning rewards is not what you would want a credit card for while your credit is bad. In this case, you'd better concentrate on credit reporting. Make sure credit card is reported to all three major credit bureaus because this will help you to build your credit history and your credit history is what your credit score's based on.