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I am an US based international student. If I take a car loan from bank to purchase an used car, will a shorter or longer repayment period have any impact on my credit score in the long run? Precisely, if I pay the loan back in 12 months vs. 60 months., which one will improve my credit score more than the other?

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The first step of credit is don't let your score dictate a decision like this. Have the lender run your credit, look at the numbers and pick the one that makes the most sense for you. If it makes the most sense for you to take a 12 month loan, take the 12 month loan. If you want some flexibility and there is no prepayment penalty, take the 60 month loan and pay it in 12 if you can. At the same APR you will pay significantly more interest over 60 months than over 12. There is no sense in paying that interest in the hopes of increasing your score a couple of points.

Agree to whatever makes the most financial sense for you, then pay on time.

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