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Hi there! I opened three new accounts recently. A US Bank Cash+, a Citi Thank You Preferred, and a Chase Sapphire Preferred. My question is, how do I avoid getting such high interest rates in the future? My lowest APR is on the Cash+ which is 16something, the Chase is 20 point something and the Citi is around 21%. My income is relatively low and I'm not super concerned cause I usually PIF every month but is there any possible way to lower these in the future?
Chase is not known for lowering APR once established. You may have luck with the other two over time.
APR's and limits are determined based on what your credit profile (and income) qualify for. If you want lower APR's then you need to identify and address the issues with your credit profile.
There is no such information in your OP so if you want feedback then you'll need to disclose some info about your profile. You can also read up and educate yourself as you'll want to be able to assess your own reports anyway. Here's a starting point but it only covers FICO scoring. It does not cover everything and it does not cover the underwriting critiera of various creditors/products (which we don't have the details for anyway).
http://www.myfico.com/crediteducation/whatsinyourscore.aspx
Chase may be difficult for lowering APR. I have a strong profile and with US Bank I've only been able to get temporary reductions so far. You can always make the request but unless your profile sufficiently changes since it was considered during approval you probably won't see results even with creditors that are willing to lower.