(a) An insurance Company has just negotiated a four-year plain vanilla swap in which it will exchange fixed payments of 10 percent for floating payments of LIBOR plus 1 percent. The notional principal is 30 million. LIBOR is expected to be 8 percent, 9 percent, 11 percent, and 13 percent (respectively) at the end of each of the next three years.

a. Determine the net dollar amount to be received (or paid) by the insurance company each year.

b. Determine the dollar amount to be received (or paid) by the counterparty on this interest rate swap each year based on the assumed forecasts of LIBOR.

(b) A Bank purchases a four-year cap for a fee of 2.5 percent of notional principal valued at $75 million, with an interest rate ceiling of 6 percent and LIBOR as the index representing the market interest rate. Assume that LIBOR is expected to be 6 percent, 7.5 percent, 9 percent, and 10 percent (respectively) at the end of each of the next four years.

a. Determine the initial fee paid, as well as the expected payments to be received by the bank if LIBOR moves as forecasted.

b. Determine the dollar amount to be received (or paid) by the seller of the interest rate cap based on the assumed forecasts of LIBOR.