$($Complex present value$)$ You are trying to plan for retirement in $12$ years, and currently you have $$100,000$ in a savings account and $$300,000$ in stocks. In addition, you plan on adding to your savings by depositing $$11,000$ per year in your savings account at the end of each of the next $6$ years and then $$22,000$ per year at the end of each year for the final $6$ years until retirement.

a$.$ Assuming your savings account returns $5$ percent compounded annually, and your investment in stocks will return $10$ 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 $8$ 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 $5$ 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.$)$