You invest $$100,000$ in a stock that trades at $$\frac{50}{?}$ share and has a P$/$E ratio of $30.$ The company's earnings grow at $10\%$ compounded annually and $5$ years later the stock is trading at a P$/$E ratio of $25.$

a$.$ Find the initial and final share prices

b$.$ Find your annualized compounded rate of return over the $5$ year investment.