Assume that you will start your career in $2$ years, and then you will work for $40$ years $($t$=42).$ When you retire, you want to be able to live entirely on your savings because you don$$t think Social Security will be around then. You want to have enough savings to pay for $$50,000$ in annual expenses for $30$ years after you retire. You think you can earn a $4\%$ return over inflation on your investments. To make it simple, assume no inflation.

a$.$ How much do you have to save per year if you save an equal amount every year?

b$.$ How much do you have to save per year if you save an equal amount every year, except you

don$$t save anything from year $5$ through year $25$ due to increased expenses due to having kids?

c$.$ How much do you have to save per year if you save an equal amount every year and invest it in

a slightly riskier investment that pays a $5\%$ return over inflation?

d$.$ How much do you have to save per year if you save an equal amount every year and invest it in

a slightly riskier investment that pays a $6\%$ return over inflation?

e$.$ Re$-$do part A$,$ but include a $20\%$ capital gains tax.