Today's value of the S&P500 stock index is at 3,915. The 500 stocks underlying the index provide an estimated dividend yield of 1.5% p.a. (continuously compounded). The risk-free rate is at 1.7% p.a. (continuously compounded).

Consider a 3-month forward contract on the S&P500 stock index.

(a) Compute today's arbitrage-free forward price of the 3-month forward contract.

Suppose you are entering today into a long position in the 3-month forward contract on the S&P500 with the forward price computed in (a).

 (b) What is the value of this long position in the forward contract today?

(c) Assume in one month the S&P500 index will be at 3,900. What will be the value of your long position in the forward contract then?