Rise and Fall

Question

The price of a stock is initially $\$1$. Each day, the stock rises by a proportion $\alpha$ (new value is $1+\alpha$ times as large) with probability $p$, or falls by a proportion $\beta$ (new value is $1-\beta$ times as large) with probability $1-p$. After $n$ days, what is the expected value of the stock price? Report the answer when $n = 10, \alpha = 0.05, \beta = 0.1,$ and $p = 1/2$ to the nearest thousandth.