A retirement planning Case In retirement planning, it is often required to determine a periodic inflation-adjusted withdrawal amount that will provide the funds necessary to maintain a desired standard of living throughout the remaining lifetime, taking into consideration the random nature of investment returns, as well as the random nature of the remaining lifetime. Consider a person who is about to turn 65 and has $1,000,000 invested in a portfolio that will provide retirement income. The return of this portfolio is expected to be normally distributed with a mean of 8% and standard deviation of 2%. Withdrawals will be made at the beginning of each year. Assume that the inflation rate will be 3%. Inflation adjustme means that the withdrawal sum would match inflation, i.e., would increase annually at the same rate as inflation. For initial analysis, assume that the retiree will live until age 95 and that the chance of the money running out before death should be limited to a maximum of 5%. 1. Determine the initial withdrawal amount (at age 60). If the retiree indeed lives until age 90. How much would be the value of the sum left over for good causes? 2. To account for the uncertainty in age at death, repeat the analysis by modelling the remaining-life expectancy as a random variable that follows a lognormal distribution with a mean of 20 and standard deviation of 10 (rounded to the nearest integer). 3. Determine how sensitive the sustainable withdrawal amount is to changes in the limiting probability of funds running out the 5% parameter that you used in your analysis so far). To do this, create an efficient frontier showing the maximum sustainable withdrawal amount as this parameter is varied from 1% to 10%. Explain clearly the meaning of efficient-frontier chart. 4. Repeat the analysis to find the initial withdrawal amount at 60 years of age if it is desired that left over sum be at least $750 thousand with a 95% probability. How much would the expected value of the left-over sum be