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When an investment changes value, the dollar amount needed to return to its initial (starting) value is the same as the dollar amount of the change - but opposite in sign. But when expressed as a Percentage gain and loss, the percentage gained will be different from the percentage lost. This is because the same dollar amount is expressed as a percentage of two different starting amounts.

Here is the same equation shown as a graph. Showing gains and losses in percentages alone does not need the actual value of the investment.

After a percentage loss, the plot shows that you always need a larger percentage increase to come back to the same value.[note 1]

Here is another way to express the same idea.[3][4] You have an initial investment of $1,000. At the end of the first year, your investment goes down by 10%. Your investment then grows by 10% at the end of the second year.

If we only wanted to know the percentage change from the initial investment to the end of the second year, the equation would look like this:[note 2]

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