I'm always amazed by people who don't bat an eye on the perspective of having a home server, sucking up electricity 24/7. In this case replacing a typical router (which consumes like a lightbulb), with a full-fledged PC (probably consuming like x100 the power). I guess some people around the world have quite cheap utility bills! For me, it's either a Raspberry Pi type of power consumption, or else a server that only…
What kind of light bulb? :) A typical consumer router will take up something like 5-10 watts. A PC will suck in 20-50. Remember that the PC will be a lot more powerful so it’ll spend most of its time with low CPU usage. Say the worst case scenario: 45W difference. 45W * (24 * 30) / 1000 = 32.4 kW*h/month. At $0.10 kWh rate that’s $3.24/month, less than a cup of Starbucks coffee.
Anyway I did the math and it would be $7/month. More than double your estimation, but still not horrendous. Although for that range of prices one might be able to find a managed instance machine in some cloud provider...
(edit: somewhere in the process I lost track of the fact this was a price _difference_ calculation, so it's adding $7 to whatever was already the cost with a more power efficient machine, which ofc. depends on number and type of HDs and other equipment)