Marcus is $25$ years old. He has a new job and intends to save $$10,000$ today and in each of the next $34$ years $(35$ deposits altogether$).$ He has decided on an investment policy in which he invests $30\%$ of his assets in a risk$-$free bond with $3\%$ continuously compounded annual interest and the remainder in the market portfolio that has lognormal returns $=12\%$ and $=35\%.$

$9.$ Marcus decides that he needs at least $$2$ million by the time he hits $60.$

$$ a$.$ Run $100$ simulations in order to determine the approximate probability of achieving this goal.

$$ b$.$ Compute the average and standard deviation of the terminal wealth.

$$ c$.$ Create a Data Table to determine the relation between the proportion invested in the risky asset and the probability of achieving the minimum at age $60.$ Set the proportions in the risky to $0\%,10\%,...,100\%.$

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