You are trying to decide how much to save for retirement. Assume you plan to save $$8,000$ per year with the first investment made one year from now. You think you can earn $11\%$ per year on your investments and you plan to retire in $31$ years, immediately after making your last $$8,000$ investment.

a$.$ How much will you have in your retirement account on the day you retire?

b$.$ If$,$ instead of investing $$8,000$ per year, you wanted to make one lump$-$sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be$?$

c$.$ If you hope to live for $27$ years in retirement, how much can you withdraw every year in retirement $($starting one year after retirement$)$ so that you will just exhaust your savings with the $27$ th withdrawal $($assume your savings will continue to earn $11\%$ in retirement$)?$

d$.$ If$,$ instead, you decide to withdraw $$200,000$ per year in retirement $($again with the first withdrawal one year after retiring$),$ how many years will it take until you exhaust your savings?

e$.$ Assuming the most you can afford to save is $$1,600$ per year, but you want to retire with $$1,000,000.00$ in your investment account, how high of a return do you need to eam on your investments?

a$.$ How much will you have in your retirement account on the day you retire?

The amount in the retirement account in $31$ years would be $$.($Round to the nearest cent.$)$