If it does (and it probably won't) it would only be a few points. To that I would say "so what?". I for one am not willing to pay what could potentially be hundreds or even thousands of dollars in interest, just to save a few points on my credit score. Were I in your shoes, I'd pay it off and then keep making my monthly payments "TO ME!" so that in the future, either I pay for what I want in cash thus avoiding having to deal with a lender at all, or at least have enough to put down more than just a "minimum" down payment on something.
Not to far back we purchased a brand new car with an asking price of $24K. With $20K cash in my hand I gave the dealer/salesman a choice.... all of it right now at this very moment in time and call it a closed deal, or I walk and never come back. That's the 2nd time in my life we've done that. Both times they took the offer.
One advantage to having paid cash for a new car (in addition to paying less for the car) was that when it came to insurance, I didn't "need" full coverage. So insurance companies were more willing to "give" a bit on their rate. For us, it was win-win-win all the way around.
