You might see a slight increase if the computer runs at full power all the time. Check your power management in the Control Panel, and set the computer to go into Standby after a certain amount of time (but definitely dissable any Hibernate / Hibernation features). Set it for something like 30 minutes to go to Standby, and then, after your done using it, after 30 minutes of innactivity, it'll go into a lower power state (hdd's, cd's, monitor, cpu, and smart fans*) will all basically power off. The memory will remain powered, to hold it's charge so when you come back to the computer, it will come back to where you left it.
I've had my laptop on for the past few months straight, just putting it into Standby when I go to sleep, or I'm at work. And I switch my desktop into Standby during those times too (unless I want to have music playing while I go to sleep).
*Smart Fans basically monitor heat to determine if they need to be running at high or low speeds, and I think, some will also switch off during standby periods.
As for the amount of increase, when running at full power all the time. It's not much. A few bucks at most. I used to run my desktop before the upgrade, at full power for months, and after I started turning it off when I wasn't using it, noticed only about $3 - $5 decrease in the electricity bill.
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