Megalopolis bank decided to issue $$150$ million of liabilities with one year to maturity to finance the purchase of $$150$ million of assets with a two year maturity. Suppose that interest rate on liabilities is $7$ percent per year and the interest rate on assets is $11$ percent per year.

a$)$ What is the bank$$s profit spread and dollar value of profit in year $1?$

b$)$ The type of risk that Megalopolis is facing is reinvestment or refinancing risk?

c$)$ If interest rates rise and Megalopolis bank can borrow new one$-$year liabilities at $15$ percent in the second year, calculate the bank$$s profit spread and dollar value of profit in year $2$

d$)$ Suppose, instead that interest rates fall and Megalopolis bank can borrow new one year liabilities at $5$ percent in the second year. What is the bank$$s profit spread and dollar value of profit in year $2?$