Suppose you want to retire in $37$ years, that you are making $$66,500$ per year today, and you are deferring $8\mathrm{.}0\%$ of your monthly gross income into your retirement plan.

a$)$ With an assumed $3\mathrm{.}7\%$ annual inflation rate from now until you retire, what net annual income will you need in your first year of retirement to maintain today$$s lifestyle?

b$)$ If your investment account earns a nominal rate of $7\mathrm{.}6\%$ per year, compounded daily, what is the effective interest rate, or annual percentage yield, of your investment account?

c$)$ Since you plan to live for another $43$ years after you retire and you want to continue the income calculated in part $($a$),$ ignoring inflation during retirement, how much should you have in your investments on retirement day, with the expectation that your account will continue to earn the effective annual interest rate found in part b$?$ Assume social security has been exhausted, you have no pension available, and you can only rely on your own personal investments to support you in retirement.

d$)$ Suppose that you$$ve accumulated $$61,000$ toward your retirement so far today. How much money should you deposit into that account every year in order to reach your goal?