Opening and closing a lot of accounts (churning) can have a negative effect on your score. For one, it significantly decreases the average age of your accounts, which makes you look like more of a risk.
It also means there are a lot of inquiries on your account - another negative factor.
Originally Posted by DallasBill
Go to MyFICO.com and pay the money and find out.
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If you are 750 or above, it won't hurt you much because that's the top tier of creditworthiness. Below that, it becomes harder to judge... because they don't release how they actually figure out your FICO score to begin with!
But if you buy your score, they will tell you the top positive and negative factors that are affecting your score, so you can get some idea.