Pay Dirt is Slate’s money advice column. Have a question? Send it to Kristin and Ilyce here . (It’s anonymous!)

Dear Pay Dirt,

When I turned 18 (25 years ago), my parents had me open a credit card in my name so I could start building credit. I never used it though—they did (responsibly, this isn’t going in that direction). The card is still open with a balance of over $4,000—they make the minimum payments to pay it off. I got another credit card for just myself about 10 years ago. I have a very good/excellent credit score. I recently received a settlement from an accident. I want to pay off the balance of that very first card and close it.

When I told my parents this, they said not to close it: Because it’s the line of credit I’ve had for the longest time, it will hurt my c

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