A DI has assets of $$10$ million consisting of $$1$ million in cash and $$9$ million in loans. The DI has core deposits of $$6$ million, subordinated debt of $$2$ million, and equity of $$2$ million. Increases in interest rates are expected to cause a net drain of $$2$ million in core deposits over the year.

a$.$ The average cost of deposits is $6$ percent and the average yield on loans is $8$ percent. The DI decides to reduce its loan portfolio to offset this expected decline in deposits. What will be the effect on net interest income and the size of the DI after the implementation of this strategy?

b$.$ If the interest cost of issuing new short$-$term debt is expected to be $7\mathrm{.}5$ percent, what would be the effect on net interest income of offsetting the expected deposit drain with an increase in interest$-$bearing liabilities?

c$.$What will be the size of the DI after the drain if the DI uses this strategy?