After graduation, you plan to work for Dynamo Corporation for $12$ years and then start your own business. You expect to save and deposit $$7,500$ a year for the first $6$ years through $t=6$ and $$15,000$ annually for the following $6$ years through $t=12.$ The first deposit will be made a year from today. In addition, your grandfather just gave you a $$32,000$ graduation gift which you will deposit immediately $).$ If the account earns $9\%$ compounded annually, how much will you have when you start your business $12$ years from now?

$$298,892$

$$286,936$

$$297,486$

$$310,848$

$$292,914$