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

Gotbucks Bank, Incorporated $($dollars in millions$)$

Assets Liabilities and Equity

Cash $ $34$ Core deposits $ $35$

Federal funds $24$ Federal funds $54$

Loans $($floating$)109$ Euro CDs $134$

Loans $($fixed$)69$ Equity $13$

Total assets $ $236$ Total liabilities and equity $ $236$

Notes to the balance sheet: Currently, the fed funds rate is $8\mathrm{.}9$ percent. Variable$-$rate loans are priced at $5$ percent over LIBOR $($currently at $12$ percent$).$ Fixed$-$rate loans are selling at par and have five$-$year maturities with $13$ percent interest paid annually. Assume that fixed rate loans are non$-$amortizing. Core deposits are all fixed rate for two years at $9$ percent paid annually. Euro CDs currently yield $10$ percent.

a$.$ What is the duration of Gotbucks Bank$$s $($GBI$)$ fixed$-$rate loan portfolio if the loans are priced at par? $($Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$

b$.$ If the average duration of GBI$$s floating$-$rate loans $($including fed fund assets$)$ is $0\mathrm{.}40$ year, what is the duration of the bank$$s assets? $($Note that the duration of cash is zero.$)($Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$

c$.$ What is the duration of GBI$$s core deposits if they are priced at par? $($Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$

d$.$ If the duration of GBI$$s Euro CDs and fed fund liabilities is $0\mathrm{.}405$ year, what is the duration of the bank$$s liabilities? $($Do not round intermediate calculations. Round your answer to $4$ decimal places. $($e$.$g$.,32\mathrm{.}1616))$

e$-1.$ What is GBI$$s duration gap? $($Do not round intermediate calculations. Round your answer to $4$ decimal places. $($e$.$g$.,32\mathrm{.}1616))$

e$-2.$ What is the expected change in equity value if all yields increase by $100$ basis points? $($Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest dollar amount.$)$

e$-3.$ Given the equity change in e$-2,$ what is the expected new market value of equity after the interest rate change? $($Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest dollar amount.$)$