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Are you on any credit borderline ? You do not show your scores so it is hard to give you an answer. If I was at least 740 I would pay off the loans , If I was 720 or less then I would not touch anything and get the loan. I would also not sign anything giving them premission to run credit. If you are borderline than get your own financing via credit union with one pull.
I ended up with 4 pulls for one car using the dealers and contrary to popular belief they dont " all count as one" Chase reports it different than Subaru so they both count. I am still wondering why Subaru runs credit as they don't offer loans they use Chase. It seems like only one pull shoudl be needed. The pulls cost me around 4 points.
If your car loan’s interest rate is low, you could get a better net return if you invest your money. If your car loan has a high interest rate, refinancing is another way to reduce your financial burden. Depending on how your credit has improved since you originally took out the loan, you could qualify for a significantly better auto loan rate. I got my car right after my student loans paid off. At that time I do not have much money so I purchased a used car from a Japanese car trading platform (https://carfromjapan.com/cheap-used-toyota-prius-for-sale-year2011). My Toyota Prius 2011 is quite good and affordable. You can consider a used car to save money.
Used car bought all cash if possible.