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If your boss tells you that you are getting a 15 percent raise, what will your new pay rate be? If your salary increases from $45,000 per year to $49,000 per year, what percent raise did you get? To answer questions like these you need to know how to calculate percent change. Once you do, the answers to such questions are easy to figure out.
What Is Percent Change?
Percent change is the amount that a quantity of something changes over time converted into a percentage. For example, if you have 100 oranges and your friend gives you 10 more, your orange supply has increased by 10 percent, because 10 is 10 percent of 100. Unfortunately, you won't always be dealing with a quantity of 100, so the calculation can be a little more difficult. Use this formula to calculate the percent change for any quantity.
Percent change = (B - A) ÷ A × 100
In this formula, A represents the original quantity -- 100 in the case of the oranges -- and B represents the final quantity -- 110 in the case of the oranges.
Negative and Positive Percent Change
Percent change calculations can give answers that are positive or negative. A negative value means that the original quantity has decreased -- that A is greater than B in the formula. A positive value means that the original quantity has increased -- that B is greater than A in the formula. Since getting a raise means that your salary or wage has increased, you will get a positive answer when you calculate the percent of a raise.
Calculating the Percent of a Raise From Old and New Wages
You can use the formula for percent change to calculate the percent of a raise if you know the wage or salary before and after the raise. Consider an individual who gets a raise from $45,000 annually to $49,000 annually. In the formula, A becomes $45,000 and B becomes $49,000. The calculation looks like this:
Percent raise = ($49,000 - $45,000) ÷ $45,000 × 100 = 8.9 percent
Calculating a New Wage From a Given Raise Percentage
What if you are told you will receive a 15 percent raise and you want to know what your wage will become? If you know your original wage, you can calculate your final wage using the formula for percent change. First you have to solve the formula for B, which represents your wage after the raise (A represents your wage before the raise). The rearranged formula looks like this:
B = A + (Percent raise ÷ 100 × A)
If your wage before the 15 percent raise was $11.25 per hour, the calculation for your wage after the raise would look like this:
Wage after raise = $11.25 + (15 ÷ 100 × $11.25) = $12.94
Timothy Banas has a master's degree in biophysics and was a high school science teacher in Chicago for seven years. He has since been working as a trading systems analyst, standardized test item developer, and freelance writer. As a freelancer, he has written articles on everything from personal finances to computer technology.
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