How do auto loans work in regards to going through a private party instead of a dealer?

Dealers usually have multiple sources to arrange a loan at competetve interest rates and have all necessary forms and documents in house so they sign you up right on the spot. Private parties have no banking license and therefore are not able to assist you with financing. They usually want cash. You must arrange your own loan

just go to your financial institution and tell them you want this car and if you have good credit they will cut you a check then you take them the title

The two choices are financing through the person selling the car, which is rare, and getting the money from a bank or credit union. I strongly recommend opening an account with a credit union if you don't have one, the rates are lower and you will be talking to a person who can authorize the loan, not someone doing paperwork for a committee. Basically, you are setting up a contract to repay the loan and pledging the car as collateral. The loan people will want to have someone examine the car as to value. The money goes directly to the seller when the title is turned over and the title has the lien recorded on it.

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