$($Complex present value$)$ You are trying to plan for retirement in $12$ years, and currently you have $$90,000$ in a savings account and $$270,000$ in stocks.

In addition, you plan on adding to your savings by depositing $$10,000$ per year in your savings account at the end of each of the next $6$ years and then $$20,000$

per year at the end of each year for the final $6$ years until retirement.

a$.$ Assuming your savings account returns $8$ percent compounded annually, and your investment in stocks will return $13$ percent compounded annually, how

much will you have at the end of $12$ years? $($Ignore taxes.$)$

b$.$ If you expect to live for $16$ years after you retire, and at retirement you deposit all of your savings in a bank account paying $11$ percent, how much can you

withdraw each year after retirement $(16$ equal withdrawals beginning $1$ year after you retire$)$ to end up with a zero balance upon your death?

a$.$ If your savings account returns $8$ percent compounded annually, how much will you have at the end of $12$ years in your savings account? $($Ignore taxes.$)$

$,($Round to the nearest cent.$)$