A forward contract is a non-standardized contract between two parties to buy or to sell an asset at a specified future time at a price agreed upon today.
The price of a forward contract is the price specified in the contract at which the long and short sides have agreed to trade the underlying asset when the contract expires.
The value of a forward contract to each side is the amount of money the counterparty would be willing to pay (or receive) to terminate the contract. Its a zero-sum game, so the value of the long position is equal to the negative of the value of the short position.
The no-arbitrage price of the forward contract (with a maturity of T years) is the price at which the value of the long side and the value of the short side are both equal to zero.
$latex FP = S_0 \times (1+R_f)^T$
The value of the short position at any point in time is the negative of the long position.