You are trying to decide how much to save for retirement. Assume you plan to save

$$$$4$ comma $0004,000$

per year with the first investment made one year from now. You think you can earn

$88\%$

per year on your investments and you plan to retire in$$

$3030$

$$years$,$ immediately after making your last

$$$$4$ comma $0004,000$

investment.

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

b$.$ If$,$ instead of investing

$$$$4$ comma $0004,000$

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

$1717$

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

$1717$th

withdrawal$($assume your savings will continue to earn

$88\%$

in$$ retirement$)?$

d$.$ If$,$ instead, you decide to withdraw

$$$$40$ comma $00040,000$

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

$$$$800800$

per$$ year, but you want to retire with

$$$$1$ comma $000$ comma $000\mathrm{.}001,000,000\mathrm{.}00$

in your investment$$ account, how high of a return do you need to earn on your$$ investments?