Ok, 10k is still alot of money. Sterling.
With 10k, you need something that gives you a rental yield.
(or 20k US dollars), but for non residents, you will need about 30% to put down.

I think your financials are out for the US.

The best market for you, or other people at this moment in time in my opinion is Egypt.

Why. It came top of rental yields when you take out taxes and inflation. The top 4 were as follows.
1. Egypt
2. Indonesia
3. Philippines
4. Panama

The US was not in sight.
With 10k you will have to take a mortgage, or you can do something with a friend.
Also, you should let it to expat people, via the internet, friends and family and work colleagues, to get 100 pounds x 24 times a year *100 pounds a week. Will give you a 10% yield on 20k apartment.

It wont make you rich, but it is a start. Alternatively you can invest in something where you live and stop paying rent. I can ask to see if anything can be brought in the US with 10k down but I dont think the rent will pay the mortgage.

Another alternative is to find another investment you are more comfortable with and invest there. ie. buying something from the US and selling in Europe.

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