Chapter 5, Problem 5.29P

A model for the movement of a stock supposes that if the present price of the stock is s, then after one period, it will be either us with probability p or ds with probability $1-p$. Assuming that successive movements are independent, approximate the probability that the stock’s price will be up at least 30 percent after the next 1000 periods if $u=1.012,d=0.990$, and $p=.52$