An investor wants to invest $$300,000$ in a portfolio of three mutual funds. The annual fund returns are normally distributed with a mean of $1\%$ and standard deviation of $0\mathrm{.}2\%$ for the short$-$term investment fund, a mean of $4\%$ and standard deviation of $2\%$ for the intermediate$-$term fund, and a mean of $5\mathrm{.}2\%$ and standard deviation of $5\%$ for the long$-$term fund. An initial plan for the investment allocation is $45\%$ in the short$-$term fund, $35\%$ in the intermediate$-$term fund, and $20\%$ in the long$-$term fund.

a$.$ Use Analysis ToolPak, with a seed of $1,$ to develop a Monte Carlo simulation with $1000$ trials to estimate the mean ending balance after the first year.

Note: Round the final answer to two decimal places.

b$.$ If the allocation is changed to $30\%$ short$-$term, $55\%$ intermediate$-$term, and $15\%$ long$-$term, estimate the ending balance after the first year.

Note: Round the final answer to two decimal places.