After graduation, you plan to work for Dynamo Corporation for $12$ years and then start your own business. You expect to save and deposit $$7,500$ a year for the first $6$ years $($t $=1$ through t $=6)$ and $$15,000$ 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 $$20,000$ graduation gift which you will deposit immediately $($t $=0).$ If the account earns $9\%$ compounded annually, how much will you have when you start your business $12$ years from now?

Group of answer choices

$$261,096$

$$324,392$

$$263,734$

$$208,350$

$$203,075$