Assume you have the following information:

consumer loans: $50$ million

commercial loans $200$ million

total assets: $250$ million

deposits: $235$ million

equity: $15$ million

total liabilities & equity: $250$ million

The average duration of the loans is $8$ years. The average duration of the deposits is $1$ year. assume interest rates are expected to increase from $10\%$ to $11\%.$ T$-$bill futures contracts are available, and the duration of the deliverable bills is $\mathrm{.}25$ years and the current price of the the futrues contract is $$96$ per $$100$ face value. Detail a strategy that completely hedges your exposure and show mathmatically that your exposure is hedged. you need to find the potential loss amount on your balance sheet, the number of futures contracts needed, and the gain of your futures portfolio