Imagine you are a 65 year-old who has just retired with financial capital (i.e. nest egg) of $1,000,000. This portfolio of financial capital is invested in an investment account that will earn a fixed 5% nominal per year (compounded monthly) for ever. You are planning to withdraw $100,000 per year from this account, in monthly increments and adjusted each month by an annualized inflation rate of 3%. Part A: Please compute the exact age at which you will run out of money. Part B: What is the minimum investment interest rate that you have to earn each year, so that your money will last forever and you never runout of money? Part C: Derive a general (or even an approximate) analytic expression for the AGE at which you will run out of money if you start with capital denoted by W and you withdraw an annual amount c (monthly), the account earn an interest rate of R nominally and the inflation rate is denoted by .