A bank has assets of $500 million with a Macaulay duration of 5 years and liabilities of $400 million with a Macaulay duration of 6 years.

What is the Macaulay duration of the equity?

If interest rates are currently at 6% by what percentage will the value of the equity change by if interest rates increase by 100 bps?

What would happen to the equity if interest rates dropped by 200 bps?

The assets are currently composed of $250 million of mortgages with a Macaulay duration of 10 years and $250 million of cash with a Macaulay duration of 0 years. There is currently no cash. What are the different steps that could be implemented to immunize the balance sheet of the bank. Calculate the amounts that would remain in each account.