Question #$2$: You are $65-$years$-$of$-$age and just retired with financial capital $($i$.$e$.$ nest egg$)$ of $$1,000,000.$ This portfolio of financial capital is invested in $$an investment account$$ that will earn a fixed $4\%$ nominal per year $($compounded monthly$)$ forever. You are planning to withdraw $$100,000$ per year from this account, in monthly increments and adjusted each month by an annualized inflation rate of $2\%.$

Part A: Please compute the exact age $($with one decimal point$)$ at which you will run out of money. Convert that into months and years.

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 run$-$out 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 $$c$($monthly$),$ the account earns an annual interest rate of $$R$$ nominally and the annual inflation rate is denoted by pie.