Use definition of the "simply-compounded spot interest rate", which is "L(t, T) = (1-P(t, T))/(r(t, T)*P(t, T))" or P(t, T) = 1/(1+L(t, T)*r(t, T)), two discount bonds P (t, T) and P (t, S) where S > T, and a no-arbitrage argument to arrive at the definition of the simply-compounded forward interest rate: "F(t, T, S) = 1/r(T, S)*(P(t, T)/P(t, S)-1)".