You buy some stock for \($1000\). After a year, you find that it has gained \(30\%\) in value. You hold it another year and find that it lost \(30\%\) from its value at the end of the first year. How much is your stock worth now? Suppose it losses \(30\%\) the first year and gains \(30\%\) the second year. Now what is it worth?

You buy some stock for \($1000\). After a year, you find that it has gained \(30\%\) in value. You hold it another year and find that it lost \(30\%\) from its value at the end of the first year. How much is your stock worth now? Suppose it losses \(30\%\) the first year and gains \(30\%\) the second year. Now what is it worth?

You would think that since the percentage gains and losses are the same over the two year period, the stock would be worth what it was originally, namely, \($1000\). But this is not how it works out.

In the first case, the stock is worth \($1000\), plus \(30\%\) of \($1000\) (\($300\)), or \($1300\) after one year. After the second year, the stock is worth \($1300\), minus \(30\%\) of \($1300\) (\($390\)), or \($910\).

In the second case, the stock is worth \($1000\), minus \(30\%\) of \($1000\) (\($300\)), or \($700\) after one year. After the second year, the stock is worth \($700\), plus \(30\%\) of \($700\) (\($210\)), or \($910\).

So despite going up and down by the same percentage, the stock lost \(9\%\) of its value.