You're good on the interest part - you don't pay the future interest if you pay in full early. Most/many personal loans follow a daily interest calc that's similar to a credit card. Take the annual rate and divide by 365 (or 360 for some) to get the daily rate and multiply that by the a balance and that's what owe in interest each day. If you pay more than is due or pay it off, you save on the future day's interest.
Some lenders extend the next due date if you pay more than is due. For example, I had a personal loan with PenFed and paid double one month to save on some interest, and when my next statemet came it showed that I could skip the next month's payment. I believe that Amex loans don't so even if you pay extra you still owe the regular payment the next month, very much like a credit card. For that reason, I usually recomment to friends and family to take the longest term that gets you the rate you want (so 36 mo instead of 12 mo) even if you can afford the higher payment that comes with the shorter term. That gives you a little cushion if you are short on funds one month since the monthly requirement payment will be lower with the longer term. You can still accelerate and pay off early without penalty.
