Any installment loans you have can help in a category often referred to as credit mix. The impact this category has on your credit score will vary based on the scoring model used. Credit mix measures your ability to maintain a consistent payment history with multiple types of credit accounts. For many young adults, student loans may be the only installment account they have on file. So when your student loan falls off your credit report, you may lose that credit mix diversity, which can temporarily lower your score.
But paying off the loan means saving the interest you are paying on the loan which may be more important than your credit score.
Remember that your credit score is just a way for a future lender to evaluate your ability to repay a loan. Paying off the loan may indeed temporarily reduce your credit score.*** But if you do apply for a loan, the lender will be looking at your debt to income ratio, and will obviously be better if you have less debt, and that is something that does not influence your credit score since the credit bureaus don't take your salary into account.
I would say it is always a good idea to pay off debt if you can, regardless of the short term impact on your credit score.
***Example: You have 2 credit cards with $5000 limits and $2000 balances, and a student loan that was originally $30,000 and is now $10,000. The scoring model sees that as you borrowing $12,000 out of a possible $40,000 credit available to you, which is 35% credit utilization. If you pay off and close the student loans, the scoring model will see you have $4000 balance out of $10,000 available to you. Thats 40% credit utilization, so your score will go down at first.
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