For investment advisors, a major consideration in planning for a client in retirement is the determination of a withdrawal amount that will provide the client with the funds necessary to maintain his or her desired standard of living throughout the client's remaining lifetime. If a client withdraws too much or if investment returns fall below expectations, there is a danger of either running out of funds or reducing the desired standard of living. A sustainable retirement withdrawal is the inflation$-$adjusted monetary amount a client can withdraw periodically from his or her retirement funds for an assumed planning horizon. This amount cannot be determined with complete certainty because of the random nature of investment returns. Usually, the sustainable retirement withdrawal is determined by limiting the probability of running out of funds to

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some specified level, such as $5\%.$ The sustainable retirement withdrawal amount is typically expressed as a percentage of the initial value of the assets in the retirement portfolio, but is actually the inflation$-$adjusted monetary amount that the client would like each year for living expenses.

Assume an investment advisor, Roy Dodson, is assisting a widowed client in determining a sustainable retirement withdrawal. The client is a $59-$year$-$old woman who turns $60$ in $2$ months. She has $$1,000,000$ in a tax$-$deferred retirement account that will be the primary source of her retirement income. Roy has designed a portfolio for his client with returns he expects to be normally distributed with a mean of $8\%$ and standard deviation of $2\%.$ Withdrawals will be made at the beginning of each year on the client's birthday.

Roy assumes that the inflation rate will be $4\%,$ based on long$-$term historic data. So$,$ if her withdrawal at the beginning of the first year is $$40,000,$ her inflation$-$adjusted withdrawal at the beginning of the second year will be $$41,600,$ and third year's withdrawal will be $$43,264,$ etc.

For his initial analysis, Roy wants to assume his client will live until age $95.$ In consultation with his client, he also wants to limit the chance that she will run out of money before her death to a maximum of $5\%.$

What is the maximum amount Roy should advise his client to withdraw on her $60$th birthday? If she lives until age $95,$ how much should the client expect to leave to her heirs?

Build a simulation model and replicate your experiment $10,000$ times for your answers. PLEASE USE EXCEL