Yes, if you close a credit card account you may lower your credit score.
Before discussing that let me correct what may be a misconception on your part. There is no family or household credit score. Each person has their own credit score. In the case of a married couple, one spouse may have an 800 score, and the other 420 depending on their repayment history. See the Bills.com resource Credit and Marriage for more on this subject.
Regarding your question, if you close a credit card account, the risk to your score is how you affect your credit utilization.
Length of Credit History
it is a common misconception that closing your card harms your score because the closed card is not factored into your length of credit history and length of credit history makes up 10% of your credit score. That is not the case; the closed card still is counted in your length of credit history for as long as it appears on your credit report, which should be 10 years after you close it.
The risk to your score when you close an account is to your credit utilization, which accoutns for 30% of your credit score. Credit utilization measures the amount of credit you use, as a percentage of the total credit you've been granted.
For example, if you have 4 credit card with total credit limits of $10,000 and you are carrying $2,000 in running balances, you would have a credit utilization of 20%. To protect your score, you want to keep your utilization below 30%, though the lower you can keep it the better.
When you close cards you reduce you total available credit If you are carrying balances on other credit cards, then you wil raise your credit utilization. Depending on the sizse of any balances and how much availalble credit you have left, it is certainly possible that you could harm your score.
Calculate what yournew credit utilization will be, if you close a card. Don't close any card if doing so will hurt your score.
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