An economic articulation would be: The future value of that asset's dividends (this could also be coupons from bonds, monthly rent from a house, fruit from a crop, etc.)
This is because we are in a risk-free situation (the whole point of the forward contract is to get rid of risk or to at least reduce it) so why would the owner of the asset take any chances?
The spot price of the asset is simply the market value at the instant in time when the forward contract is entered into.
Doing some reduction we end up with: Notice that implicit in the above derivation is the assumption that the underlying can be traded.
There is a difference between forward and futures prices when interest rates are stochastic.