$1.$ Assume that you are $23$ years old and plan to retire when you are $66$ years old, that is$,43$ years from now. Your personal long term $($strategic$)$ investment goal is to accumulate $$2\mathrm{.}5$ million at the time you retire. Your opportunity cost of capital $($discount rate$)$ is $10\mathrm{.}25$ percent.

a$.$ How much must you save each year to attain your long$-$term retirement goal assuming your first savings will be made at the end of each year.

b$.$ What would be your maximum withdrawal from your personal investment account if you plan to exhaust your personal savings at age $90?$

c$.$ The projected average rate of inflation $($for a full employment economy$)$ is $3$ percent and unfortunately, inflation will affect your withdrawal amount. How would inflation affect your annual withdrawal? Show the detailed amortized schedule for this problem.

d$.$ You realize that your strategic investment plan which is a road map of attaining your goal is uncertain and risky when you quantify the uncertainties. Discuss some of the risks $($both inherent and external$)$ that may affect the attainment of your goal.