The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, we can express the forward price in terms of the spot price and any dividends. For forwards on nontradeables, pricing the forward may be a complex task.
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Contents
Forward Price Formula
If the underlying asset is tradable and a dividend exists, the forward price is given by:
where
 is the forward price to be paid at time
 is the exponential function (used for calculating continuous compounding interests)
 is the riskfree interest rate
 is the cost of carry
 is the spot price of the asset (i.e. what it would sell for at time 0)
 is a dividend that is guaranteed to be paid at time where
Proof of the forward price formula
The two questions here are what price the short position (the seller of the asset) should offer to maximize his gain, and what price the long position (the buyer of the asset) should accept to maximize his gain?
At the very least we know that both do not want to lose any money in the deal.
The short position knows as much as the long position knows: the short/long positions are both aware of any schemes that they could partake on to gain a profit given some forward price.
So of course they will have to settle on a fair price or else the transaction cannot occur.
An economic articulation would be:
 (fair price + future value of asset's dividends)  spot price of asset = cost of capital
 Forward price = Spot Price  cost of carry
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.) is calculated using the riskfree force of interest. This is because we are in a riskfree 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? He would reinvest at the riskfree rate (i.e. U.S. Tbills which are considered riskfree). The spot price of the asset is simply the market value at the instant in time when the forward contract is entered into. So OUT  IN = NET GAIN and his net gain can only come from the opportunity cost of keeping the asset for that time period (he could have sold it and invested the money at the riskfree rate).
let:
 K = fair price
 C = cost of capital
 S = spot price of asset
 F = future value of asset's dividend
 I = present value of F (discounted using r )
 r = riskfree interest rate compounded continuously
 T = length of time from when the contract was entered into
Solving for fair price and substituting mathematics we get:
where:
(since where j is the effective rate of interest per time period of T )
where c_{i} is the i ^{th} dividend paid at time t ^{i}.
Doing some reduction we end up with:
Notice that implicit in the above derivation is the assumption that the underlying can be traded. This assumption does not hold for certain kinds of forwards.
Forward versus Futures prices
There is a difference between forward and futures prices when interest rates are stochastic. This difference disappears when interest rates are deterministic.
In the language of stochastic processes, the forward price is a martingale under the forward measure, whereas the futures price is a martingale under the riskneutral measure. The forward measure and the risk neutral measure are the same when interest rates are deterministic.
See Musiela and Rutkowski's book on Martingale Methods in Financial Markets for a continuoustime proof of this result. See van der Hoek and Elliott's book on Binomial Models in Finance for the discretetime version of this result.