$1.$ Interest Rate Risk: Bank Dylan balance sheet is listed below. Market yields and durations $($in years$),$ respectively, are in parenthesis. The amounts are in millions.

Assets Liabilities and Equity

Cash $$20$ Demand deposits $$250$

Fed funds $(1\mathrm{.}05\%,0\mathrm{.}02)150$ MMDAs $(2\mathrm{.}5\%,0\mathrm{.}50)($no minimum balance requirement$)360$

T$-$bills $(5\mathrm{.}25\%,0\mathrm{.}22)300$

T$-$bonds $(7\mathrm{.}50\%,7\mathrm{.}55)200$ CDs $(4\mathrm{.}3\%,0\mathrm{.}48)715$

Consumer loans $(6\%,2\mathrm{.}50)900$ CDs $(6\%,4\mathrm{.}45)1,105$

C&I loans $(5\mathrm{.}8\%,6\mathrm{.}58)475$ Fed funds $(1\%,0\mathrm{.}02)515$

Fixed$-$rate mortgages $(7\mathrm{.}85\%,19\mathrm{.}50)1,200$ Commercial paper $(3\%,0\mathrm{.}45)400$

Variable$-$rate mortgages, repriced @ quarter $(6\mathrm{.}3\%,0\mathrm{.}25)580$ Subordinated debt:

Fixed rate $(7\mathrm{.}25\%,6\mathrm{.}65)200$

Premises and equipment $120$ Total liabilities $$3,545$

Equity $400$

Total assets $$3,945$ Total liabilities and equity $$3,945$

a$.$ What is Bank duration gap?

b$.$ Use these duration values to calculate the expected change in the value of the assets and liabilities of Bank for a predicted increase of $1\mathrm{.}5$ percent in interest rates.

c$.$ What is the change in equity value forecasted from the duration values for a predicted increase in interest rates of $1\mathrm{.}5$ percent?