Consider an FI that issues $$100$ million of liabilities with one year to maturity to finance the purchase of $$100$ million of assets with a two year maturity. Suppose that the cost of funds $($liabilities$)$ for the FI is $5$ percent per year and the interest return on the assets is $8$ percent per year.

a$.$ Calculate the FI$$s profit spread and dollar value of profit in year $1.$

b$.$ Calculate the profit spread and dollar value of profit in year $2,$ if the FI can refinance its liabilities at $5$ percent.

c$.$ If interest rates rise and the FI can borrow new one$-$year liabilities at $9$ percent in the second year, calculate the FI$$s profit spread and dollar value of profit in year $2.$

d$.$ If interest rates fall and the FI can borrow new one$-$year liabilities at $3$ percent in the second year, calculate the FI$$s profit spread and dollar value of profit in year $2.$