StarBank has the following balance sheet $($in millions$)$:

Assets : Liabilities and Equity:

Cash required reserves $$2$ Deposits $$8$

Loans $$10$ Long$-$term debt $$2$

Equity $$2$

Total assets $$12$ Total liabilities and equity $$12$

The average interest earned on the loans is $5\mathrm{.}3$ percent and the average cost of deposits is $6$ percent. Rising interest rates are expected to induce a net deposit drain of $+38\mathrm{.}2$ percent. Borrowing more debt will cost the bank $5\mathrm{.}5$ percent in the short term.

a$)$ What will be the cost of using a strategy of purchased liquidity management to manage the deposit drain?

b$)$What will be the size of the bank if a purchased liquidity management strategy is adopted?