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

$\backslash$table$[[$Gotbucks Bank Inc. $($dollars in millions$)],[$Assets$,$Liabilities and Equity,$],[$Cash$,$$$30,$Core deposits,$$20],[$Federal funds,$20,$Federal funds,$50],[$Loans $($floating$),105,$Euro CDs$,130],[$Loans $($fixed$),65,$Equity,$20],[$Total assets,$$220,$Total liabilities,$],[,,$and equity,$$220]]$

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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$,R(1+R)=0\mathrm{.}01$ for all assets and liabilities.$)$