The new bank TAR started its first day of operation with a capital of $6$ million USD and received $100$ million USD in savings deposits. The bank issued a commercial loan worth USD $25$ million and another USD $25$ million as collateral. a$)$ If the required reserve is $8\%$ of deposits, what does the bank's balance sheet look like? b$)$ TAR Bank decides to invest $45$ million USD in government bonds. What does the balance sheet look like? c$)$ On the third day of operation, deposits decreased by USD $5$ million. What does the balance sheet look like? Are there any problems? d$)$ To meet the shortfall in the previous question, TAR bank will borrow cash on the interbank market. What does the balance sheet look like after this transaction?