Investments in the Stock Market have increased at an average compound rate of about $5\%$ since $1900.$ It is now $2013.$ a$)$ If you invested $$1,000$ in the stock market in $1900,$ how much would that investment be worth today? b$)$ If your investment in $1900$ has grown to $$1,000,000,$ how much did you invest in $1900?$