College Expenses Dan works during the summer to help with expenses at school the following year. He is able to save $$100$ each week for $12$ weeks, and he invests it at $1\%$ compounded weekly.

a$)$ How much does he have after $12$ weeks?

b$)$ When school starts, Dan will begin to withdraw equal amounts from the account each week. What is the most Dan can withdraw each week for $34$ weeks?

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