a link to this article grabbed my Interest as I was browsing the site for something totally unrelated to finance.
Your question is not silly - I'm not a financial expert, but I've been in your situation several times with Carmax Auto Finance (CAF) in particular.
A lot of people probably thought you don't understand how financing works - but your Car Loan set up is EXACTLY how CAF Financing works, which I've used several times. Just some background info to anyone else reading this - unlike most other Simple Interest Car Financing, with CAF, they calculate per-diem based on your principal balance, and recalculate it every time you make a payment, regardless of when your actual due date was.
But here's what makes CAF financing particularly fair - when you do make a payment, your per-diem since your last payment accrued X dollars, and that's your interest portion that is subtracted first from your payment (and obviously per-diem goes down faster the more you pay in a payment), and then EVerything else, including Any extra payments you make - goes to Principal. You do not have to specify that the extra payment(S) are principal only. If your payment amount per month is $500 and you give them 11 payments of $500 - the first $500 will have a small portion go to interest accrued since the last payment - depending on the per-diem that was recalculated, and then EVERYTHING ELSE goes to principal and STILL PUSHES YOUR NEXT DUE DATE (I prefer to break up extra payments as precisely the amount due per month, so that my intention is clear - pay the extra as a payment for the next month, and the one after that, etc, and keep pushing my next due date). That last point of pushing your next due date is the key - not all car financing companies do that. A lot of them will let you pay to principal yes, but you're still due next month. With CAF, you can have your cake, and eat it too. I worked for them in College - I know their financing system in and out, and I've always financed with them for that very reason.
So, back to the question - should you keep the loan alive, albeit for a small amount. My unprofessional answer is yes! Car loans are very powerful in your credit report because they are installment accounts (same as Mortgages, and other accounts that you pay down to 0 and the loan is closed). Credit cards, are revolving accounts, and don't offer as much bang for your money - unless you are savvy in manipulating your card balances - take it up one month, take it down to 0 the next month, etc. I play those games a lot - but I always find mortgage and auto loans make the best impact.
I do exactly what you do myself - I pay off the car down to about $500 (I actually make several small payments each equal to the agreed upon Monthly payment because their system automatically treats that as a payment for the next month due, and the one after that, etc - on top of paying it all to principal as I mentioned).
DO NOT leave a dollar, as another reader mentioned - they have a "good will" threshold, I can't remember how much - probably $50, for which they will consider the account paid off, and close it out. So, if your concern is throwing away free money but you still want the account alive, your "sweet spot" where you can be sure the loan is not closed, is probably around $100.
BUT....something else important to consider if you decide to go with that strategy of keeping the account alive (which I recommend). In my case, CAF will adjust down your next payment due, if it's less than the principal left. SO, let's say your regular payment is $400 and you only leave a $100, your next payment due is $100 (and it will go up a few cents each month because of the small per-diem), and that is exactly what CAF will report to the credit bureaus as your monthly obligation - which sucks because now your awesome car payment history looks like you've only been paying $100 every month - so, leave something close to one month's payment (yes, the interest accrued will be higher - but I'm not a penny-pincher when the reward is worth it - if you left $400 for 1.5 years at 10% APR - that equates to about $50 interest for that entire time - well worth it in my books.
Sorry for rambling a lot, I suck myself into these debates all the time :)