An investor who buys 100 shares for $40 a share of a stock that pays a per-share dividend of $2 annually signs up for the dividend reinvestment plan. If neither the price of the stock nor the dividend is changed, how many shares will the investor have at the end of ten years?

Hint: Each share pays a dividend sufficient to buy another 1/20 of a share. This means that at the end of any given year, Investor will have 1.05 times the number of shares held at the beginning of such year.

In other words, at end of first year, Investor has 100 x 1.05 shares; at end of 2nd year, has 100 x 1.05^2 shares;...

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