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 $2\%$ and standard deviation of $0\mathrm{.}3\%$ for the short$-$term investment fund, a mean of $5\%$ and standard deviation of $3\%$ for the

intermediate$-$term fund, and a mean of $6\mathrm{.}2\%$ and standard deviation of $6\%$ 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.

Mean ending balance after the first year

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.

Mean ending balance after the first year

c$.$ Compare the two investment strategies in parts a and $b$ and choose the most appropriate answer from the following choices.

On average, the investment strategy in part a is more risky and yields a lower return.

On average, the investment strategy in part a is less risky and yields a higher return.

On average, the investment strategy in part a is less risky but yields a lower return.

On average, the investment strategy in part a is more risky but yields a higher return.