a$)$ A given bank has the following interest$$sensitive assets and liabilities on its balance sheet $($in million Kwacha$).$

Interest Rate Sensitive Assets Interest Rate Sensitive Liabilities

Government Securities $150$ Time Deposits $469$

Loans $575$ Saving Deposits $200$

If the interest rates rise by $1\mathrm{.}5\%,$ what is the change in net interest income assuming a parallel shift in the yield curve? Define the maturity bucket approach as an extension to the gap analysis, and how it can be used to manage interest rate risk.

b$)$ A bank has $$100$ million in earning assets, a net interest margin of $5\%,$ and a $1-$

year cumulative GAP of $$10$ million. Interest rates are expected to increase by $2\%.$

If the bank does not want net interest income to fall by more than $25\%$ during the next year, how large can the cumulative GAP be to achieve the allowable change in net interest income?