$(9$ points$)$ The following is an FI's balance sheet $($$millions$).$

$\backslash$table$[[$Assets$,$Amount,Duration,Liabilities,Amount,Duration$],[$Cash$,$$$1,0$ years,Dem. Deposits,$$100,0$ years$],[$FF&RP$,20,0\mathrm{.}01$ years,FF&RP$,50,0\mathrm{.}01$ years$],[$Munis$,50,x1\mathrm{.}94,$CDs$,90,1\mathrm{.}0$ years$],[$Loans$,200,y0\mathrm{.}25,$Net Worth,${31}^{**},]]$

Notes to Balance Sheet:

Munis are $2-$year $6$ percent annual coupon municipal notes selling at par. Loans are floating rates, repriced quarterly. Spot discount yields for $91-$day Treasury bills are $3\mathrm{.}75$ percent. CDs are $1-$year pure discount certificates of deposit paying $4\mathrm{.}75$ percent. Hint: The duration of all floating rate debt instruments is equal to the time to repricing of the instrument.

a$.$ What is the duration of the municipal notes $($the value of $x)?$

b$.$ What is this bank's interest rate risk exposure, if any?

c$.$ What will be the impact, if any, on the market value of the bank's equity if all interest rates

increase by $75$ basis points? $($i$.$e$.,\frac{R}{1+R}=0\mathrm{.}0075)$