1) A bank can borrow or lend at LIBOR. Suppose that the 6-month rate is 5% and the 9-month rate is 6%. The rate that can be locked in for the period between 6 months and 9 months using an FRA is 7%. What arbitrage opportunities are open to the bank? All rates are continuously compounded.

2) An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding.

3) The 6-month, 12-month, 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5%, with semiannual compounding. (a) What are the rates with continuous compounding? (b) What is the forward rate for the 6-month period beginning in 18 months? (c) What is the value of an FRA that promises to pay you 6% (compounded semiannually) on a principal of $1 million for the 6-month period starting in 18 months? 102 CHAPTER 4

4) What is the 2-year par yield when the zero rates are as in Problem 3? What is the yield on a 2-year bond that pays a coupon equal to the par yield?