Wirelessly posted (Mozilla/5.0 (iPhone; U; CPU iPhone OS 4_3_2 like Mac OS X; en-us) AppleWebKit/533.17.9 (KHTML, like Gecko) Version/5.0.2 Mobile/8H7 Safari/6533.18.5)
To answer your question, most likely you will have to pay the full, unsubsidized price.
If your current iPhone 4 is in good condition, consider selling it and using that money to buy the white one - honestly why extend your contract for a simple color change.