Why is the value of a forward contract discounted to the present value?

I'm not sure if this question has been asked before, but it's a simple one. Let's consider a Forward contract on a non-income paying investment asset. We know that the Forward price on such an asset is given by:

$K=S_oe^{rT}$

which we can get through no-arbitrage arguments. Suppose this contract were entered into today, at $t=0$ and is concluding at time $t=T$. Then, the value of the Forward contract at any time $t$ between $t=0$ and $t=T$ is given by:

$f=(F_o-K)e^{-r(T-t)}$

What I don't understand is why the $e^{-r(T-t)}$ part is included into the equation? Since $K$ of the forward contract is a fixed price that was negotiated when the contract was entered into (i.e at time $t=0$), shouldn't we just compare it with the Forward Price of the asset (and not discount it)?

• At time T. But then doesn't it not matter whether we discount it or not. It's sort of like just looking at it on a different scale. – ricksanchez Jun 16 '18 at 23:29

Because the amounts $F_0$ and $K$ are both paid at time $T$. So you know this contract will be worth $F_0 - K$ at time $T$, but if you want to know what it is worth at time $t$ you have to discount it.