It's still not your cheapest option in many ways, but sometimes. Cheap enough is good.
With a 3-year reserved instance, using the "intensive usage" pricing (since it's always on), and in the cheapest availability zone. I get a price of 6.42$/month. I guess in practice, even for an personal thing, around 10GB of storage would be required (1$) (does the installed OS counts towards this number ?). Add 10GB of transfered data (1$), as a vpn/screen server is unlikely to have huge amounts of incoming data.
The final price is 8.42$. Which, for a 600MB ram server, is quite competitive. If I didn't forget something.
This is about the only use case where I would recommend AWS, though. Starting at ~25/30$, there are way better alternatives (including cheap dedicated). And if you need more bandwidth, cheap VPS tend to come with 20 or 100GB/month at least. But you'd get less RAM.
If you don't need much, http://www.lowendbox.com/ is a good site to see what's out there.
I have 2 cores (well, shared box..), 1GB of ram, 20 GB of hdd. I don't quite remember what option I selected for bandwidth, but the hoster's TOS say 'if you exceed your bandwidth limit, we'll throttle you to 10MBit. No additional charges apply'. Uhm.. Fine.
I pay 11 EUR, which is awfully close to your price without any commitment (I can cancel every month) and with better specs.