$9.$ Use the data provided for Gotbucks Bank Inc. to answer this question.

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Notes to the balance sheet: Currently, the fed funds rate is $8\mathrm{.}5$ percent. Variable$-$rate loans are priced at $4$ percent over LIBOR $($currently at $11$ percent$).$ Fixed$-$rate loans are selling at par and have five$-$year maturities with $12$ percent interest paid annually. Core deposits are all fixed rate for two years at $8$ percent paid annually. Euro CDs currently yield $9$ percent. $($LG $23-3)$

a$.$ What is the duration of Gotbucks Bank$$s $($GBI$)$ fixed$-$rate loan portfolio if the loans are priced at par?

b$.$ If the average duration of GBI$$s floating$-$rate loans $($including fed fund assets$)$ is $0\mathrm{.}36$ year, what is the duration of the bank$$s assets? $($Note that the duration of cash is zero.$)$

c$.$ What is the duration of GBI$$s core deposits if they are priced at par?

d$.$ If the duration of GBI$$s Euro CDs and fed fund liabilities is $0\mathrm{.}401$ year, what is the duration of the bank$$s liabilities?

e$.$ What is GBI$$s duration gap? What is its interest rate risk exposure? If all yields increase by $1$ percent, what is the impact on the market value of GBI$$s equity? $($That is$,\backslash$Delta R$/(1+$ R$)=0\mathrm{.}01$ for all assets and liabilities.$)$