$$ share of United Parcel Service stock $($UPS$)$ is currently selling for $$150.$ pension

fund manager is planning to purchase $1,000$ shares in three months. He is concerned

that the price will rise by then. To hedge this risk, he enters into a forward contract

to buy $1,000$ shares of UPS in three months. Assume that the risk$-$free rate is $1\%$

$(PR,$ continuous compounding$).$

Calculate the appropriate price per share at which the pension fund manager

can contract to buy UPS in three months.

$$ ssume that two months into the contract the UPS stock price is $$140.$ Calculate

the pension fund manager's gain or loss from the forward contract.

Suppose that at expiration, the price of the stock is $$175.$ Calculate the pension

fund manager's gain or loss from the forward contract.