Unless government supervision is installed,
every year food prices will continue to rise by approximately 20% annually.
A. every year food prices will continue to rise by approximately 20% annually: every year + annyally = redundant
B. every year food prices have continued to rise by approximately 20%: this is a prediction, so we need the future tense, "will". We should not use the present perfect "have continued".
C. food prices will continue to rise by approximately 20% every year: correct answer.
D. food prices would continue to rise every year by approximately 20%: would is a conditional as well as the simple past of "will". The tense in the subordinated clause "unless...is installed" is the the present, so we need to use the future "will continue to rise"
E. food prices will continue to increase in number by approximately 20% annually: this version is wordy and awkward. The phrase "increase in number" is unnecessarily wordy.