There are a lot of credit card offers for people with bad and limited credit and some offers even come with rewards programs. For example, you can choose Discover it® Secured card. This card requires a refundable security deposit, but allows you to earn cash back on purchases, including on Google store purchases. This card has no annual fee. As a bonus, Discover matches cash back you’ve earned at the end of first usage year (if you are a new cardmember). So, you may be able to offset your deposit by cash back rewards.
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All rates and fees, and other terms and conditions of the products mentioned in this article/post are actual as of the last update date but are subject to change. See the current products' Terms & Conditions on the issuing banks' websites.