$r_t -.01 = .4(r_{t-1} - .01) + .3(r_{t-2}-.01) + .23(r_{t-3} - .01) + a_t$
I found $E[r_t] = .01$ and that $r_t$ is weakly stationary.
Now, $Var(r_t) = E[r_t^2] - E[r_t]^2$ so I just need to find $E[r_t^2]$.
$E[r_t^2] = E[r_t(.01 +.4(r_{t-1} - .01) + .3(r_{t-2}-.01) + .23(r_{t-3} - .01)]$
$= .01^2 + .4\gamma_1 + .3\gamma_2 + .23\gamma_3 + \sigma_a^2$
where do I go from here? I am having the same problem in solving for the covariances ($\gamma_l = Cov(r_t, r_{t-l}$) where I don't know what to do for $E[r_tr_{t-k}]$