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Part $1$

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

$$$$7$ comma $5007,500$

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

$66\%$

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

$3838$

$$years$,$ immediately after making your last

$$$$7$ comma $5007,500$

investment.

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

b$.$ If$,$ instead of investing

$$$$7$ comma $5007,500$

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

$1919$

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

$1919$th

withdrawal$($assume your savings will continue to earn

$66\%$

in$$ retirement$)?$

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

$$$$90$ comma $00090,000$

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$ comma $5001,500$

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?