Amy is now $($year $0)25$ years old and planning for her retirement at age $65.$ She would like to have $$2$ million for her retirement by then. She will make her first deposit in her retirement savings account next year $($year $1)$ and continue until her last deposit at age $65($year $40).$ All deposits are made on the last day of the year. Amy expects her income to increase at an annual rate of $2\mathrm{.}86\%($nominal$)$ and thus will increase her savings at the same rate. Her savings will earn an annual return of $6\mathrm{.}23\%($nominal$).$

Use the above information to answer questions $($A$)($C$).$

A$.$ What should be Amy's first deposit to achieve her goal for the retirement savings account?

B$.$ Suppose that inflation is $2\mathrm{.}34\%$ per year. What would be the real value of Amy's retirement savings account balance when she retires $($year $40)?$

C$.$ Suppose that inflation is $2\mathrm{.}86\%$ per year $($rather than $2\mathrm{.}34\%$ as noted above$),$ and there is no change in Amy's income growth and the return on her savings. What would Amy's first deposit $($in nominal terms$)$ have to be in order to achieve the same real value in her retirement savings account balance when she retires?