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

Gotbucks Bank, Incorporated $($dollars in millions$)$Assets$$Liabilities and Equity$$Cash$ $49$Core deposits$ $42$Federal funds$39$Federal funds$69$Loans $($floating$)124$Euro CDs$149$Loans $($fixed$)84$Equity$36$Total assets$ $296$Total liabilities and equity$ $296$

Notes to the balance sheet: Currently, the fed funds rate is $10\mathrm{.}4$ percent. Variable$-$rate loans are priced at $2$ 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. 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?

Note: Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161)$

b$.$ If the average duration of GBI$$s floating$-$rate loans $($including fed fund assets$)$ is $0\mathrm{.}55$ year, what is the duration of the bank$$s assets? $($Note that the duration of cash is zero.$)$

Note: 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?

Note: Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161)$

d$.$ If the duration of GBI$$s Euro CDs and fed fund liabilities is $0\mathrm{.}420$ year, what is the duration of the bank$$s liabilities?

Note: 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?

Note: 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?

Note: 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?

Note: 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.