Conduct duration gap analysis using the following information:

$\backslash$table$[[$Assets$,$Amount,Rate,Macaulay's Duration$],[$Cash$,$$$23,000,0\%,0],[$Bonds$,$$$102,000,7\mathrm{.}2\%,1\mathrm{.}8$ years$],[$Commercial loans,$$375,000,11\mathrm{.}0\%,1\mathrm{.}5$ years$]]$

Wabilitles & Equity

$\backslash$table$[[$Small time deposits,$$130,000,3\mathrm{.}6\%,4\mathrm{.}0$ years$],[$Large CDs$,$$$70,000,6\mathrm{.}3\%,1\mathrm{.}0$ year$],[$Transactions accounts,$$250,000,2\mathrm{.}8\%,3\mathrm{.}3$ years$],[$Equity$,$$$50,000,,]]$

a$.$ Calculate the bank's duration gap if the ALCO targets the market value of stock holders' equity. Is this bank positioned to gain or lose if interest rates rise?

b$.$ Estimate the change in market value of equity if all market interest rates fall by an average of $1\mathrm{.}5$ percent. Compare the results by applying Equation $6\mathrm{.}2$ to each balance sheet item and adding versus using Equation $6\mathrm{.}9.$

c$.$ Provide a specific transaction that the bank could implement to immunize its interest rate risk. The transaction may be a new asset funded by a new liabilitv or an asset