How to calculate reverse percentage

If you have a starting amount and you want to add a percentage, you can simply multiply the per cent by the original amount to find the amount that gets added. This, for example, would occur if you need to calculate how much sales tax or tip to add to the bill. But, if you have only the final amount and want to know the percentage added, you need to work in reverse to find the original amount based on the percentage added and the final amount. For example, you would do this if you had the final cost and the percentage of sales tax, but you wanted to know the cost before the tax.

Divide the percentage added to the original by 100. For example, if a sales tax of 6 per cent was added to the bill to make it £137, divide 6 by 100 to get 0.06.

Add 1 to the percentage, expressed as a decimal. In this example, add 1 to 0.06 to get 1.06.

Divide the final amount by the result of Step 2 to find the original amount before the percentage was added. In this example, divide £137 by 1.06 to find the amount before the sales tax was added, which equals £130.

Subtract the original amount from the final amount to find the amount added. Completing the example, subtract £130 from £137 to find that £7 was added.

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About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."

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