How to Calculate Total Percent Change
When you have a series of percent changes--increases, decreases, or both--the final percent change is a function of the individual increases and decreases. Computing the total percent change is a multiplicative process, not an additive one. A common mistake is to simply add and subtract the percent increases and decreases to find the total change, however, this leads to the wrong answer.
For example, consider an item priced at $100. If the price increases by 20%, then decreases by 30%, then increases again by 10%, what will the final price be?
To compute the final price, you express a 20% increase as a factor of 1.2, a 30% decrease as a factor of 0.7, and a 10% increase as a factor of 1.1. Then the correct answer is found by multiplication:
$100(1.2)(0.7)(1.1) = $92.40,
which represents a total percent decrease of 7.6%. (This is because $100 - $92.40 = $7.60, and $7.60/$100 = 7.6%.) If you simply added and subtracted the percents, you would end up with 0% change, which is incorrect.
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