I am studying DSGE models and try to solve exercise 2.2 from Gali's (2008) book. In short, consider the simple classical economy where the following approximate equilibrium conditions must be satisfied: $$y_t = E_t\{y_{t+1}\} - \frac{1}{\sigma}(i_t - E_t\{\pi_{t+1}\} - \rho)$$ and $$r_t = i_t - E_t\{\pi_{t+1}\}$$ and $y_t$ and $r_t$ determined independently of monetary policy.
Derive an interest rate rule that guarantees full stabilization of inflation (i.e. $\pi_t = \pi^* \;\; \forall t$).
I thought of the simple rule like $i_t = \phi\pi_t$. It is possible to show (using forward iteration) that in this case $$\pi_t = \sum_{i=0}^{\infty}\frac{1}{\phi^{i+1}}E_t\{r_{t+i}\}$$ and letting $\phi \to \infty$ inflation goes to zero. However, I think that this not what was meant by the author. Any help appreciated.