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

Gotbucks Bank, Inc. $($in $ millions$)$

Assets Liabilities and Equity

Cash $ $33$ Core deposits $ $30$

Federal funds $23$ Federal funds $53$

Loans $($floating$)108$ Euro CDs $133$

Loans $($fixed$)68$ Equity $16$

Total assets $ $232$ Total liabilities and equity $ $232$

Notes to the balance sheet: Currently, the fed funds rate is $8\mathrm{.}8$ 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. Assume that fixed rate loans are non$-$amortizing. Core deposits are all fixed rate for two years at $8$ percent paid annually. Euro CDs currently yield $9$ 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$.,32\mathrm{.}161))$

Duration

$4\mathrm{.}037$

years

b$.$

If the average duration of GBI$$s floating$-$rate loans $($including fed fund assets$)$ is $\mathrm{.}39$ year, what is the duration of the bank$$s assets? $($Note that the duration of cash is zero.$)($Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$

Duration $($assets$)$

$1\mathrm{.}403$

years

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$.,32\mathrm{.}161))$

Duration $($deposits$)$

$1\mathrm{.}926$

years

d$.$

If the duration of GBI$$s Euro CDs and fed fund liabilities is $\mathrm{.}404$ years, what is the duration of the bank$$s liabilities? $($Do not round intermediate calculations. Round your answer to $4$ decimal places. $($e$.$g$.,32\mathrm{.}1616))$

Duration $($liabilities$)$

years

e$-1.$

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

Duration gap

years

e$-2.$

What is the expected change in equity value if all yields increase by $200$ basis points? $($Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations.$)$

Expected change in equity value $

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.$)$

New market value $