I have Windows XP and I was wondering when XP support ends, will I have to purchase a new computer?
That depends on your computer. It may be possible for you to upgrade to Windows 7 or 8.
System requirements for Windows 7 are at least 1GHz 32-bit (x86) or 64-bit (x64) processor , 1GB RAM (32-bit) or 2 GB RAM (64-bit), 16 GB available hard drive space (32-bit) or 20 GB (64-bit) and DirectX 9 graphics device with WDDM 1.0 or higher driver .
System requirements for Windows 8 are 1 GHz or faster processor with support for PAE, NX and SSE2, 1GB RAM (32-bit) or 2 GB (64-bit), free drive space of 16 GB (32-bit) or 20 GB (64-bit) and Microsoft DirectX 9 graphics device with WDDM drive. You will also need a screen resolution of at least 1024 x 768 and an Internet connection to access the Windows Store. Plus a Microsoft Account may be required for some purposes.
You can check your device’s compatibility with the Windows 7 Upgrade Advisor by clicking here. 
Or its compatibility with Windows 8 by clicking here.  On this page, you’ll see both the Windows 8.1 Upgrade Assistant and the Windows 8 Upgrade Assistant. The 8.1 Upgrade Assistant won’t work with XP – but the Windows 8 assistant should. The requirements for 8 and 8.1 are virtually identical.
Time again for the reminder that official Microsoft support Windows XP ends on April 8, 2014. That means no more security updates or bug fixes for XP. That also means that third-party security programs cannot guarantee the safety of Windows XP and the system is expected to be a big target for viruses and malware.