Gunnison Bank has issued an $18$ month, $$6$ million CD paying $11$ percent to fund $18$ months loan paying an interest rate of $10$ percent. The principal of the loan will be paid in three installments: $$2$ million in first $6$ months, $$2$million in $12$ months and the balance at the end of the $18$ months.a$.$ What is the maturity gap of Bank?b$.$ Assuming no change in interest rates over the year, what is the expected net interest income at the end of the year?c$.$ What would be the effect on annual net interest income of a $3$ percent interest rate increase that occurred immediately before the loan was made? What would be the effect of a $2$ percent decrease in rates after the loan was made?d$.$ What do these results indicate about the ability of the maturity model to immunize portfolios against interest rate exposure? $(30$ marks$)$