In the following linear AR(1) model, rt is the log price of a security at time t. r_t = 0.004 + r_(t-1) + a_t, here at is a random process obeying normal distribution N(, 2) with mean and variance 2, such as the following a_t iid N(0, 0.36). Assume further that r100 = 3.865.

Compute the 95% interval forecast for r101 at the forecast origin t = 100.