The following balance sheet information is available $($amounts in thousands of dollars and duration in years$)$ for a financial institution:

Treasury bonds are five$-$year maturities paying $6$ percent semiannually and selling at par.

a$.$ What is the duration of the T$-$bond portfolio?

b$.$ What is the average duration of all the assets?

c$.$ What is the average duration of all the liabilities?

d$.$ What is the leverage$-$adjusted duration gap? What is the interest rate risk exposure?

e$.$ What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of $0\mathrm{.}5$ percent $[$i$.$e$.,\frac{R}{1+R}=0\mathrm{.}0050?$

f$.$ If the yield curve shifts downward $0\mathrm{.}25$ percent $[$i$.$e$.,\frac{R}{1+R}=-0\mathrm{.}0025],$ what is the forecasted impact on the market value of equity?

g$.$ What variables are available to the financial institution to immunize the balance sheet? How much would each variable need to change to get DGAP to equal $0?$