Multiple choice exam solution: emphasising math

Question

I am designing a multiple choice question exam and I would like for the correct answer to be emphasized in the standardized bold way. The issue is that some of the answers contain only mathematics.

Here is a MWE:

\documentclass[addpoints]{exam}
\printanswers

\begin{document}

\begin{questions}
\question Which of these guys invented time?
    \begin{choices}
        \choice Stephen Hawking 
        \choice Albert Einstein
        \choice Isaac Newton
        \correctchoice This makes no sense
    \end{choices}

    \question
    What is the way to write down the function for cubic power?
    \begin{choices}
        \choice  $f(x) = x$
        \choice  $f(x) = x^2$
        \correctchoice  $f(x) = x^3$
        \choice  $f(x) = x^4$
    \end{choices}
\end{questions}

\end{document}

This, however, leads to the math option not being bolded:

I've tried to redesign the appearance of the correct option using \CorrectChoiceEmphasis{\boldmath}, but this does not provide the appropriate solution for two reasons: 1) I have to redefine it before every question with mathematical answer and then return back to the original definition, 2) The option mark (in this case "C.") is not bolded:

Is there a way to set the emphasis automatically so that both text and math are bolded in the correct solution?