To find the contestant's balance of prize money, we can start by calculating the total amount lost due to the 6 wrong answers.
The contestant loses $12.50 for each wrong answer. Since he answered 6 questions wrong:
\[ \text{Total loss} = \text{Number of wrong answers} \times \text{Loss per wrong answer} \]
\[ \text{Total loss} = 6 \times 12.50 \]
Calculating that:
\[ \text{Total loss} = 75 \]
Since the contestant has answered no questions correctly, his balance of prize money is:
\[ \text{Balance} = 0 - \text{Total loss} \] \[ \text{Balance} = 0 - 75 = -75 \]
Thus, the contestant's balance of prize money is \(-$75.00\).