2. Modified Duration Gap. Round your answers to 2 decimal places for this question. (7 marks in total) Bank NYC has the following balance sheet in market value: Assets (mil$) Liabilities (mil$) Cash 20 Demand Deposits 60 3-yr Loans 100 1-yr Debt 50 Equities 10 Total Assets 120 Total Liab. & Eqt. 120 Further information:

(1) There is no default risk in both the 3-yr Loans and the 1-yr Debt.

(2) The 1-year Debt is a zero-coupon debt with yield 5%.

(3) In questions (a)-(f), assume that the 3-year Loan is a fixed coupon loan, which pays 10% coupon each year. The payment is made once per year. Currently this loan is priced at par.

A) Which is the (leveraged adjusted) modified duration gap of this bank? (3 marks)

B) If the market interest rate is expected to increase by 0.5% for all maturities, what is the expected impact on the bank's net worth? (2 marks)

C) Suppose instead of a coupon loan, the 3-year Loan is an annually amortizing loan. That is, the borrowers of this loan will pay the bank equal payment each year (NOT monthly) throughout the life of this loan. The interest rate the bank charges on this loan is still 10% and the market value of this loan is still 100 mil$. What is the modified duration of this amortizing loan? (2 marks)