$2.$ After graduation, you plan to work for Tesla for $12$ years and then start your own business. You expect to save and deposit $$16,000$ a year for the first $6$ years $($t $-1$ through t $6)$ and $$5,300$ annually for the following $6$ years

$($t $=7$ through t $=12).$ The first deposit will be made a year from today. In addition, your grandfather just gave you

a $$30,000$ graduation gift which you will deposit immediately $($t $-0).$ If the account earns $6\%$ compounded annually, how much will you have when you start your business $12$ years from now? $(20$ points; Show all your work for partial credit. Note that correct answers without any work will be rewarded ZERO, no exceptions.$)$