You should look for secured credit cards. These cards are created for those who have a negative credit history, but they want to improve their credit score. Secured credit cards require a collateral deposit. Otherwise, the secured credit cards work just like unsecured credit cards, and may even offer bonus programs.
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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.