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Part $1$

$($Complex present value$)$ You are trying to plan for retirement in $88$years$,$ and currently you have $ $120$ comma $000$$$120,000$ in a savings account and $ $360$ comma $000$$$360,000$ in stocks. In$$ addition, you plan on adding to your savings by depositing $$$$11$ comma $00011,000$ per year in your savings account at the end of each of the next $44$ years and then $$$$22$ comma $00022,000$ per year at the end of each year for the final $44$ years until retirement.

a$.$ Assuming your savings account returns $77$ percent compounded$$ annually, and your investment in stocks will return $1212$ percent compounded$$ annually, how much will you have at the end of $88$years$?($Ignore$$ taxes.$)$

b$.$ If you expect to live for $1818$ years after you$$ retire, and at retirement you deposit all of your savings in a bank account paying $1010$percent$,$ how much can you withdraw each year after retirement $(1818$ equal withdrawals beginning $1$ year after you$$ retire$)$ to end up with a zero balance upon your$$ death?

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Part $1$

a$.$ If your savings account returns $77$ percent compounded$$ annually, how much will you have at the end of $88$ years in your savings$$ account? $($Ignore$$ taxes.$)$

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