The balance sheet for Gotbucks Bank Inc. $($GBI$)$ is presented below $($$ millions$).$

Liabilities and Equity Assets

$20$$ Core deposits $30$$ Cash

$50$ Federal funds $20$ Federal funds

$130$ Euro CDs $105$ Loans $($floating$)$

$20$ Equity $65$ Loans $($fixed$)$

$220$$ $$220$ Total assets

Notes to the balance sheet: The fed funds rate is $8\mathrm{.}5$ percent, the floating loan rate is LIBOR $($London Interbank Offered Rate$)+4$ percent, and currently LIBOR is $11$ percent. Fixed$-$rate loans have fiveyear maturities, are priced at par, and pay $12$ percent annual interest. The principal is repaid at maturity. Core deposits are fixed rate for two years at $8$ percent paid annually. The principal is repaid at maturity. Euro CDs currently yield $9$ percent.

a$.$ What is the duration of the fixed$-$rate loan portfolio of Gotbucks Bank?

b$.$ If the duration of the floating$-$rate loans and fed funds is $0\mathrm{.}36$ year, what is the duration of GBI$$s assets?

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

d$.$ If the duration of the Euro CDs and fed funds liabilities is $0\mathrm{.}401$ year,

what is the duration of GBI$$s liabilities?

e$.$ What is GBI$$s duration gap?

What is its interest rate risk exposure?

f$.$ What is the impact on the market value of equity if the relative change in all interest rates is an increase of $1$ percent $(100$ basis points$)?$

Note that the relative change in interest rates is $\backslash$Delta R$/(1+$ R$)=0\mathrm{.}01.$ g$.$ What is the impact on the market value of equity if the relative change in all interest rates is a decrease of $0\mathrm{.}5$ percent $(50$ basis points$)?$ h$.$ What variables are available to GBI to immunize the bank? How much would each variable need to change to get DGAP to equal zero?