You are helping a manager calculate the present value a single cash$-$flow at the end of the year. Based on your conversation with this manager you gather that $\backslash (\backslash$mathrm$\{$s$\}/\backslash$mathrm$\{$he$\}\backslash )$ believe the expected cash$-$flow is $\backslash (\backslash$$ $5,000\backslash ).$ S$/$he also feels that that any $\backslash (1\backslash \%\backslash )$ deviation of the S$\backslash$&P$500$ rate of return from its mean will cause a corresponding deviation of $\backslash (\backslash$$ $500\backslash )$ in the cash$-$flow. The risk free rate is $\backslash (5\backslash \%\backslash ),$ and the expected rate of return on the index is $\backslash (12\backslash \%\backslash ).$ What is the present value of this cash$-$flow?

Numeric Response