QwerkyPengwen :
You won't be changing mobo because it's only worthwhile then to upgrade to newer platforms and you'll need to buy DDR4 RAM.
So for your budget you can look around ebay, or local used market for a deal on a 4th gen i7. If you have a Z series motherboard then get a K series 4th gen i7.
An i7-4770/4770k is what you're looking for.
Depending on your motherboard you may be able to use the i7-4790/4790k with a BIOS update. But you have to Google that and make sure
here is my system info my mobo is from a Packard bell imedia s2985 so a mobo upgrade is what I had in mind due to not being able to update the bios.
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System Manufacturer Packard Bell
System Model iMedia S2985
System Type x64-based PC
System SKU
Processor Intel(R) Core(TM) i3-4170 CPU @ 3.70GHz, 3700 Mhz, 2 Core(s), 4 Logical Processor(s)
BIOS Version/Date American Megatrends Inc. P11-B4, 11/06/2015
SMBIOS Version 2.8
Embedded Controller Version 255.255
BIOS Mode UEFI
BaseBoard Manufacturer Packard Bell
BaseBoard Model Not Available
BaseBoard Name Base Board
Platform Role Desktop
Secure Boot State Off
PCR7 Configuration Binding Not Possible
Windows Directory C:\Windows
System Directory C:\Windows\system32