There is a 120-day futures contact on a stock. The current stock price is $50.00 and the stock is expected to pay a dividend of $0.20 in 20 days, and $0.20 in 110 days. The annual risk-free rate is 5%. Assume there are 365 days in a year and continuous compounding.

(a) Calculate the no-arbitrage futures price of this contract.

(b) Assume the futures price in the contract is equal to the no-arbitrage price you computed in (a). After 60 days, the stock price is $45.50. Calculate the value of the contract to the long and short positions, assuming the risk-free rate is still 5%. Assume there are 365 days in a year and continuous compounding.