Question 1. A bank is offering a commercial loan to a company for $10m at an interest rate of 5% APR to be paid off in monthly payments over the next 5 years. a) Find the monthly payments the bank will charge the company as repayment of the loan.

b) Suppose the company is willing to increase its monthly payments at a growth rate of 2% APR (monthly growth rate of 2%/12) in exchange for reducing the loan repayment period. How many months will it take to pay off the $10m loan?

Question 2. The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0 (view the T-bill as zero-coupon bond). A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.

Question 3. Consider the zero and forward rates in the table below. Assume that both rates are continuously compounded.

Time-to-maturity (in years) Zero rates (% per annum) Forward rates (% per annum)

1 3.0

2 4.5 X

3 Y 5.8

a) Find the forward rate in the cell labeled X (the forward rate over period [1 year, 2 year]).

b) Find the zero rate in the cell labeled Y (the zero rate of maturity 3 years).

c) A company enters into an FRA that specifies it will receive a fixed rate of 5% (annually compounded) on a principal of $10 million for a one-year period stating in two years. Find the value of the FRA.