If the initial value of a forward contract is zero, surely the forward price used would be the spot price at the time the contract was created?
However, my notes tell me that the forward price F, at $t = 0$ for delivery at time $t = T$, is given by $F = e^{rT}S_{0}$ where r is the risk-free rate and $S_{0}$ is the spot price at $t = 0$.
Why is this?