Alex needs to withdraw an amount of $15,000 at the end of her first month of retirement from an investment account that generates an annual rate of return of 7.8%, compounded monthly. Afterwards, she continues her monthly withdrawals with the amount growing at a monthly inflation rate of 0.35% over her expected retirement horizon of 22 years. Assume 360-day year and 30-day month in your analysis!

(a) State the cash flow pattern and explain your correct choice of interest rate, i.e., EAR/EPR/PER for Alex's monthly withdrawals. Calculate the minimum beginning balance of the investment account required for meeting her retirement needs.

(b) Assume now that Alex has cumulated a nest egg of $3,500,000 in the investment account upon her retirement, calculate the amount of inheritance she can leave for her children at her passing, given your answer in (a).

(c) Calculate the maximum fixed amount that Alex's descendants can withdraw quarterly from the investment account indefinitely, given your answer for the inheritance in (b).