<prompt> Human: Hi guys, I have a 20k loan at 2.99 interest from USAA. I havent made any payments on it yet so the loan balance is now 20240.13 since my military pay hasnt started yet, but it will start in the next month. As soon as I am done with this loan, I plan to take the monthly payment I would have spent, and immediate invest it into a mutual fund or index fund or something. There are no early prepayment penalties for my loan. I took a look at some amortization schedules, and if I pay it off in 4 years, I pay 447.81 a month for 48 months, only paying 1259.66 in interest. If I pay in 5 years, I pay 363.60 for each month, and pay 1575.79 in interest. Im not entirely sure how me spending 80 more each month only saves me 316.13 over the long run. Can someone explain the math to me? I feel like im in some sort of logical fallacy or math riddle I cant get  <response>: Whenever you make a payment youre paying the interest that accrued since the last payment and then towards the principal. So if you pay down more principal with each payment the interest payments are smaller, leading to you paying more principal, which in turn makes interest payments less. So the faster you pay it the less time interest has to accumulate and the less interest youll have. Leading to a smaller interest payment. The reason its only saving you 363.60 dollars is because thats the difference in interest payments from paying it off faster. The principal is still just a large no matter if you pay it off in 48 months or 60 months. 363.60 is just the interest that isnt allowed to accumulate since you paid it off faster.The math behind amortization schedules is based on sums of geometric series. So its kind of hard to grasp, but its all just algebra. 