Though not an option for everyone, teaching English abroad can be a good way to pay off student loans. I have never had any loans, but I was able to save enough to put myself though a decent 4 year university in a few years time by working overseas.
Working overseas can be exciting as well as challenging. I have lived in for extended period of time outside of the US (ten years total in 2 different countries). My reason for leaving the US was NOT to escape student debt as some have done. I do not recommend defaulting on your responsibilities. But it is possible to pay off your loans while traveling and seeing & doing amazing things at the same time. I taught English abroad for 10 years. Here are some tips from my personal experiences.
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1) You can make TONS of money with the right qualifications
Good teachers are in demand all over the world. Good teachers that speak perfect English are in higher demand. English teachers get a bad rap as being unqualified vagabonds in a lot of places, but if you show up on any country's doorstep with a degree in any field, you can probably find a job.
If you want to stick with English a great place to start is international schools. It's hard to find reliable native English speakers who can commit to living more than one year outside their home country. If you could sign a 2+ year contract, you've already got a foot in the door. Teach anything from preschool to high school, or even university courses (depending on the country).
You can do the same thing with a degree in many other subjects. Science, math, sports – whatever else you find in a regular school in your home country, there's going to be a position in every international school in every country. There's plenty of jobs out there.
The advantage of working for an international school is that you often get wages that match those of your home country, but live in a place where the cost of living is cheaper. This obviously won't work for moving to the UK from the US, or from Canada to any Western European nation. But the entire rest of the world is a possibility.
When I was in Prague I freelanced and made about 18,000 CZK per month, or about 1,000 USD, which was pretty good for teaching salaries at that time (the Czech teachers probably made 1/3 of that). The sports teacher in the British international school made 3 times what I was making. Too bad I never got into that gig, but I didn't have the qualifications.
2) There's tons of opportunities to freelance
If you REALLY need to save money, there's not enough hours in the day for all the English teaching opportunities you will have. In addition to your teacher's position and the 8:00 – 4:00 schedule (or 1/2 day schedule in some cases), you can teach on the side.
You could teach English, which I did, and is in huge demand in most countries, or you could teach something you are good at (in English). I knew a guy that taught guitar to expats. I knew a girl that gave singing lessons too. I taught math lessons for a bit as well. Private tutoring is possible too – parents would LOVE their kids learning stuff while listening to English. The possibilities are endless. It's really just a matter of getting your foot in the door, and the word will spread as you put your feelers out.
For example, sometimes I would get off in the afternoon and squeeze in about 3 lessons in the evening. Occasionally I'd fit some work in on the weekends, and would basically double my salary just by working harder. I was super busy and unable to maintain it for more than about 6 months without burning out, but I made bank.
3) Tax advantages
Both countries I worked in paid me under the table, meaning I paid zero in local taxes. The US exempts you from paying any Federal taxes for anything under $96k if you are working overseas, and that most likely exempts you from state tax as well. You'll still have to pay social security.
4) Save more
Public transportation is much better in many places in the world (or at least more widely available), and the driving is too crazy to even want to attempt it in other places. This means no car payment, no car insurance, no gas, company provided health insurance, no income tax, no property tax, and probably cheap (or free) rent, in addition to the lower cost of living. Rather than pay $1200 a year for car insurance, you pay 50 cents per motorcycle ride (if you're in Southeast Asia), or a couple buck a month for a tram ticket (in Europe).
You are now saving double or triple what you would be saving at home.
All this budgeting may sound stressful, but having a ‘short sprint' of an intense 2 or 3 year budget can help you pay a huge chunk of, if not, your entire student loan in a short amount of time. It's a good budgeting strategy to go through spurts, or phases, where you budget hard. Then you can relax your tight budget for a while and enjoy life, then budget more. It's been proven somewhere, but I can't find the article.
Just take my word for it. You'll just have to remind yourself to stay away from the alcohol and partying that goes on among the travel communities. It sucks that you'll be traveling and missing out on a lot of cool stuff, but you'd be surprised at how much culture you can take in just by sitting for an afternoon in a coffee shop or people watching in a park.
It's less impressive on Facebook, but just as interesting IMO.
More about my personal budget
In addition to doing all of the above things, I also started a profitable website on the internet. This may seem out of reach to many of you that have never created a website before, but it's actually a lot easier than you think.
I've written about how to do this about a million times on this blog, so I won't go into detail. If this interests you, I can teach you. But the point is that the major money maker for me was being able to make US dollars while living in a low-cost-of-living country. Imagine making $500 per day where is costs you $5 per day to eat!
How Do I Get Started?
People complain about having too much student debt, and about how there are no good jobs. We all have options. If moving to an exotic country where you are qualified for a variety of high paying positions, you can live off $500 per month, have the chance to travel, meet people, & learn new skills, and beer costs $1 does not sound appealing to you, I think you need to rethink your priorities.
A great place to start your search for jobs is Daves ESL Cafe. It's an amazingly poorly designed website for how old it is, but it gets the job done and is super active with jobs. It's probably the most famous ESL jobs board online. You also might want to think about getting some ‘Teaching English as a Secon Language' certification. The two main types are TEFL and TESOL. Many countries don't require any proof that you have them though, so you could probably print a fake one depending on where you go and how confident you are.
PS. You'll need a resume for applying for jobs.