To find the contestant's balance of prize money, we first need to calculate how much he lost for answering 6 questions wrong.
The contestant loses $12.50 for each wrong answer. Therefore, for 6 wrong answers:
\[ \text{Total loss} = 6 \times 12.50 = 75.00 \]
Since he has not answered any questions correctly, his total balance of prize money becomes:
\[ \text{Balance} = 0 - 75.00 = -75.00 \]
Thus, the contestant's balance of prize money is \(-$75.00\).
The correct response is: \(-$75.00\)