$($Future value of an annuity and annuity payments$)$ You are trying to plan for retirement in $10$ years, and currently you have $$180,000$ in a savings account and $$300,000$ in stocks. In addition, you plan to deposit $$11,000$ per year into your savings account at the end of each of the next $5$ years, and then $$14,000$ per year at the end of each year for the final $5$ years until you retire.

a$.$ Assuming your savings account returns $9$ percent compounded annually, and your investment in stocks will return $13$ percent compounded annually, how much will you have at the end of $10$ years? $($Ignore taxes.$)$

b$.$ If you expect to live for $19$ years after you retire, and at retirement you deposit all of your savings into a bank account paying $12$ percent, how much can you withdraw each year after you retire $($making $19$ equal withdrawals beginning one year after you retire$)$ so that you end up with a zero$-$balance at death?

a$.$ Assume your savings account returns $9$ percent compounded annually, and your investment in stocks will return $13$ percent compounded annually.

How much will you have at the end of $10$ years in your savings account? $($Ignore taxes.$)$

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

How much will you have at the end of $10$ years for your investment in stocks? $($Ignore taxes.$)$

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

Therefore, how much will you have at the end of $10$ years?

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

b$.$ If you expect to live for $19$ years after you retire, and at retirement you deposit all of your savings into a bank account paying $12$ percent, how much can you withdraw each year after retirement $(19$ equal withdrawals beginning one year after you retire$)$ to end up with a zero balance upon your death?

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