$($a$)$ You are saving for retirement, and you can afford to save $$12,600$ every year, starting one year from today. If you invest for $30$ years earning an average return of $6\mathrm{.}24\%$ per year, how much will you have saved for your retirement?

$($b$)$ How much would you have in your retirement account if you began these same $30$ annual payments immediately?

c$).$ Suppose that once you retire, you want to be able to withdraw $$78,000$ per year $($starting one year from your retirement$)$ for a total of $25$ years during your retirement. How much would you need to have in your account when you retire to make this work assuming an annual interest rate of $6\mathrm{.}24\%?$

$($d$)$ How much would you need to have in your retirement account if you began these same $25$ annual withdrawals immediately?

$($e$)$ Changing the scenario, now let$$s assume that you want to have $$1,400,000$ in your retirement account at the end of $30$ years. You have now decided that you will deposit funds at the end of every month for $30$ years. The interest rate is still $6\mathrm{.}24\%$ per year. How much do you need to deposit each month in order to reach your goal in $30$ years.?