[nakia674]

When dealing with interest, is the present value always smaller than the future value?

[ArcSine]

Consider the fundamental relationship between the future value FV and the present value PV of some amount, where there are n periods between the two:

for some interest rate r.

Now starting with the premise that present value is no less than future value...

PV ≥ FV

get that inequality boiled down to a statement involving r only, to see what must be true of the interest rate r in order to have present value greater than or equal to future value. Then ask yourself when, if ever, do interest rates satisfy that condition?

Hint to get you started: First substitute for FV in the inequality, its equivalent expression in terms of PV, which is the RHS of the previous equality. Then divide both sides of the inequality by PV, assuming that present value is some positive quantity.