Jim is investing in his company$$s $401($k$)$ retirement plan, funding $6\%$ of his salary to get a $3\%$ match $($thus effectively investing $9\%$ of his annual salary$).$ He invests in each of the three available funds. $50\%$ of his contributions go into investment A$,$ which has an average return of $6\mathrm{.}91\%$ with a standard deviation of $12\mathrm{.}89\%.$ The rest of his contributions are equally divided between investment B$,$ which has an average return of $8\mathrm{.}94\%$ with a standard deviation of $15\mathrm{.}21\%,$ and investment C$,$ which has an average return of $9\mathrm{.}88\%$ with a standard deviation of $17\mathrm{.}14\%.$ Jim is currently $24$ years old and earns $$55,000$ this year, but anticipates a pay raise of$,$ on average, $2\mathrm{.}83\%$ with a standard deviation of $0\mathrm{.}72\%.$ Develop a simulation model to predict his $401($k$)$ balance at age $60.$ Ensure you iterate your simulation multiple times $($between $400$ and $20,000).$