Suppose that the interest rate $r$ is a random variable.
Given a future value $FV$, the expected present value is $\mathbb E (\frac{FV}{1+r})$.
Given a present value $PV$, the expected future value is $\mathbb E ((1+r)PV)$.
What's with the inconsistency? i.e. why shouldn't I calculate the expected PV by $\frac{FV}{\mathbb E (1+r)}$ in the first case?
To address some of the comments - I understand that $\mathbb E (XY) \neq \mathbb E (X)\mathbb E (Y)$. What I'm asking is the seeming inconsistency. To give a numerical example, suppose the interest rate is either 5% or 10% with probabilities 0.3 and 0.7. Then the present value of 100 is 0.3(100/1.05) + 0.7(100/1.1) = 92.2. But the future value of 92.2 is 92.2 * (0.3 * 1.05 + 0.7 * 1.1) = 100.04. Not 100. Why is this the case?
They are already consistent, try $PV = E_F(E_P) = E_F((1+r)PV) = PV$.