1. Assume perfect competition (reasonable assumption for analysis), no firm invests (I) today unless tomorrows revenue (R) is higher than the investment.
3. In perfect competition, I = R because both firms (or any number of n firms) will invest up to a point just below I > R.
This is wrong. Firms will invest to the point where their revenue equals the natural rate of interest, which is determined by peoples time preferences.
That is, firms do not only require that R>I to invest. They require that R>k*I where k would be the natural rate of interest. Money today is worth more than money tomorrow. Interest rates are the market price for time, and that price is not 0 as you assume.