Will having a paid auto loan in my credit history benefit when I try to get a mortgage in the future?

Right now my credit rating is a little over 800. The only things in my credit history are 2 current credit cards. I am also about to buy a new car and am trying to figure out if it will be better for me in the future (when I am trying to buy a house) if I get an auto loan or if I just pay the car myself.

So if I get the minimum car loan, and just pay it off over 2 years, it will cost me around $ 478 in interest. So, assuming the fact that for like the next 3 or 4 years my credit rating were to remain the same, which would be better for my credit when I try to get a home loan? Is paying almost $ 500 now (well, over 2 years) to get an auto loans payments/history in my credit report going to benefit me or not?

If it will get me a lower interest rate on a mortgage I’ll be all for it. If it won’t make a difference, then I probably wouldn’t want to spend the extra $ 500ish. Anyone happen to know? Thanks!
I never had any payments on my current car. It was gifted to me by my parents. (It is 23 years old)

I’ve heard both that having an auto loan can hurt you when you try to get a home loan and that it can help you because you have credit history in multiple areas. (ie. credit cars + loans vs just credit cards) So I’m not really sure which is true or if both are in different circumstances.

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