Just because there is no Aeropostale MasterCard, it doesn’t mean that you won’t be able to collect rewards for your shopping. I’m assuming the “basic credit card” you have is offered by a major bank. What you should do is find out about all of the credit cards that are offered by that bank. Many banks will offer at least one card that allows you to collect points on purchases. For example, if you look at one of the rewards cards that are offered by Discover, you will see that their card allows you to collect cash back on virtually any purchase. The cash back you collect can be redeemed on a wide range of options such as travelling or shopping.
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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.