Which option will save you the most money in the long run? That is tough. Assuming you stay healthy, don't lose your job, don't experience a pay cut or any major emergency that drains your savings, then applying the $6000 to the higher interest loan will save you more money in the long run.
However, the difference in savings is a few hundred dollars. Not much really. So, in this case, I'd put the $6k towards the smaller loan. Why? Because then you'd pay it off faster. Once that's done, you open up your cash flow by the minimum monthly payment you would have had on that loan.
Assuming they both have the same or similar number of months left, by paying the smaller loan off sooner, you'd open up $X month, where $X is your minimum monthly payment. This could be useful to you if you want to take on some other debt (like buying a house) because it lowers your debt to income ratio. If you put that money towards the higher loan, your DTI won't change until the normal time you would have paid off the smaller loan. Even if you are not looking to purchase anything that requires you to have a lower DTI, paying the smaller loan off sooner increases your cash flow sooner (because your monthly payment on the higher loan doesn't change just because you lowered the balance by $6k). So you'd be more robust to emergencies if your current income doesn't allow for much savings.
A major emergency could wipe out all savings from paying down the bigger balance. So, I'd suggest:
- Make sure your savings is built up before making a lump payment towards the loan, since lowering the balance won't change your monthly payment and if you have no savings, all it takes is one costly emergency to wipe out savings from paying to loan early by forcing you to borrow money at potentially higher rates, or destroying your credit because you can't borrow and necessarily pay late/default on your loan obligations.
- Consider the benefit of increased cash flow and lower DTI that will come from paying off the smaller balance, lower rate, loan early relative to the several hundred you might save in interest by paying down the higher rate loan.
Edit: TripeHound asked a question, pretty much requesting more details for why I was biased towards paying off the smaller loan first. What follows is my response, with a bit of reorganization:
Typically, people asking these questions don't have so much wealth that "which loan to pay first?" is an academic question. They need to make smart financial decisions. While paying the highest interest loan saves the most money in interest - that only occurs under the assumption that nothing bad will ever happen to you until the loans are paid off. In reality, other things happen. Tires blow out, children get sick, you get laid off and so the "best" thing to do is the one that maximizes your long term financial health, even if it comes at the expense of a few $k more interest.
Each loan has a minimum monthly payment. Let's assume, barring any windfalls of additional cash, you will just make the minimum payments each month towards a loan. If you pay off the smaller loan first, that increases your available monthly cash flow. At that point, you can put extra towards the other loan. However, if an emergency should come up, or you need to save for a vacation, you can do that, without negatively impacting the second loan, because you'd just drop back to its minimum payment.
Putting the money towards the higher balance loan would mean it takes you longer to reach this point as the time to reach payoff on the first loan will not change ($6k only reduces the $25.6k loan to $19.6k) so you never gain the flexibility of additional cash flow until the time you would have paid off the $13.5k originally. I'd rather have a few hundred dollars each month that I can choose to use to make additional loan payments, eat out, pay for car repairs, pay for emergencies than be forced to dip into credit or worse, pay day loans, should an emergency happen.