(I work in finance)
I have never seen anybody have a problem, in your situation, with having the loan end when they send that last payment in. Generally they won't require you to keep making payments.. they would actually enjoy it very much if you waited 5 months, because that is a long time for them to be building interest. However when it comes time to send in that last payment, for $200 or $1300 or however much, most lenders will go ahead and terminate the loan, send you title, etc. HOWEVER, this does vary from lender to lender and you will want to give them a call. Loads and loads of people make extra payments.. they will be familiar with the situation (or call right back and talk to somebody who's not new if they sound oblivious).
Most do not "hold" your payment to apply later down the road. They apply it, but give you a large grace period before requiring you to make another payment. If you sent them $1400 and your loan balance reflected only a minimum payment you are dealing with a different situation.. you need to call them and ask them to backdate previous payments to principle only and inquire as how to make future apply. If that is your situation, be careful to not apply ALL of your payments to principle only, as this may cause some of your interest due to become "late" and incur a fee. Many people at customer service centers won't have been there long enough to be familiar with how their company treats this, I recommend speaking with several people including a manager before making the change.