Assume that the First National Bank has the balance sheet shown below, the income gap is currently -$17.5 million, and that interest rates are initially at 10%.

	Assets	Duration		Liabilities		Duration
Reserves	5,000,000	0
Securities				Checkable Deposits	15,000,000	2
<1 Year	5,000,000	0.4		Money Market Deposits	5,000,000	0.1
1 to 2 Years	5,000,000	1.6		Savings Accounts	15,000,000	1
>2 Years	10,000,000	7		CDs
Residential Mortgages				Variable-rate	10,000,000	0.5
Variables-rate	10,000,000	0.5		< 1 Year	15,000,000	0.2
Fixed-rate	10,000,000	6		1 to 2 Year	5,000,000	1.2
Commercial Loans				> 2 years	5,000,000	2.7
< 1 Year	15,000,000	0.7		Interbank Loans	5,000,000	0
1 to 2 Years	10,000,000	1.4		Borrowings
> 2 years	25,000,000	4		<1 Year	10,000,000	0.3
Buildings, etc	5,000,000	0		1 to 2 Year	5,000,000	1.3
				> 2 years	5,000,000	3.1
				Bank Capital	5,000,000
Total	100,000,000			Total	100,000,000

1. Calculate the duration gap for the bank.

2. If the First National Bank sells $10 million of its securities with maturities greater than two years and replaces them with securities maturing in less than one year, what is the income gap for the bank? What will happen to profits next year if interest rates fall by 3 percentage points? 

3. Given the estimates of duration above, what will happen to the bank’s net worth if interest rates rise by 10 percentage points? Will the bank stay in business? Why or why not?

4. If the manager of the First National Bank revises the estimates of the duration of the bank’s assets to four years and liabilities to two years, what is the effect on net worth if interest rates rise by 2 percentage points?

5. Given the estimates of duration in Problem 4, how should the bank alter the duration of its assets to immunize its net worth from interest-rate risk?

6. Given the estimates of duration in Problem 4, how should the bank alter the duration of its liabilities to immunize its net worth from interest-rate risk.