I have been doing this with my game server for years.
First of all, pretty much every mobo made in the last 4 years supports a wake up timer in the BIOS.
Enter BIOS (usually) by pressing delete as system boots. Go to something called Power Management Setup, Under the heading Wake Up By Alarm, you can enter the date you want the computer to start, or enter a zero for daily startup. Next under Time, enter time of day (military time) you want computer to start (16:00 would be 4:00pm).
To turn off, I used to use a program called switchoff. I've since learned that it is a simple matter to run shutdown as a Scheduled Task.
First create a shutdown shortcut, paste this code into the command line of a new shortcut (created by right-clicking on your desktop):
%windir%\System32\shutdown.exe -s -t 0
When you run that shortcut it will immediately shut down your computer. (the zero at the end of that code regulates how many seconds to wait before shuttdown, you can create a delay prior to shutdown by adding more seconds there).
Now schedule that shortcut to be run:
Go to:
Programs/Accessories/System Tools/Scheduled Tasks
Browse to where you placed your shutdown shortcut.
Done.