The forward pricing model states that two investors should be indifferent between paying P for a j+k year zero coupon, $1 FV contract and paying the PV of a j year zero coupon $1 FV forward contract maturing in k years at a price of Fj+k.
P(j+k) = PjF(j,k)
Or F(j,k) = P(j+k)/Pj
The forward rate model relates forward and spot rates as follows:
[1 + S(j+k)](j+k) = (1 + Sj)j [1 + f(j,k)]k
[1 + f(j,k)]k = [1 + S(j+k)](j+k) / (1 + Sj)j
This equation suggests that the forward rate f(2,3) should make investors indifferent between buying a five-year zero-coupon bond versus buying a two-year zero-coupon bond and at maturity reinvesting the principal for three additional years.
If the yield curve is upward sloping, [i.e., S(j+k) > Sj], then the forward rate corresponding to the period from j to k [i.e., f(j,k)] will be greater than the spot rate for maturity j+k [i.e., S(j+k)]. The opposite is true if the curve is downward sloping.