The value of the S&P 500 index is 2,050. The risk-free rate is 5% and the continuous dividend yield is 2.5%. Calcula te the no-arbitrage price of a 210-day forward contract on the index. Assume continuous compounding and there are 365 days in a year.

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

(b) Assume the forward price in the contract is equal to the no-arbitrage price you computed in (a). After 120 days, the value of the index in the previous example is 1,980. Calculate the value to the long position of the forward contract, assuming the risk-free rate is still 5% and the continuous dividend yield is 2.5%.