Investments in the stock market have increased at an average compound rate of about $5\%$ per year since $1900.$

a$.$ If you invested $$1,000$ in the stock market at the beginning of $1900,$ how much would that investment be worth in $2011?($Round your answer to the nearest cent.$)$

Investment value in $2011$

$$44,761\mathrm{.}66$

b$.$ If your investment is a sum of money in $1900($beginning of the year$)$ that has grown to $$1$ million in $2011,$ how much did you invest in $1900?($Round your answer to the nearest cent.$)$

Investment value in $1900$

$$44,761\mathrm{.}66$