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Math Help - percentages - taxing problem

  1. #1
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    percentages - taxing problem

    Hi, can someone help?
    I need to calculate a sum in Japanese yen that includes a 20.42% tax charge.

    After the 20.42% is deducted, the net received sum should be 1,135,000 yen.
    So how much should the gross invoice be for?

    Simply adding 20.42% of the final sum will not give the correct fee because when tax is deducted it will be calculated on the gross, not the net amount.

    More to the point, what's the process to figure this out?

    Many thanks!

    (I'm just using a calculator, sorry, don't understand algebra!)
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  2. #2
    MHF Contributor
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    Re: percentages - taxing problem

    Divide the net sum (1,135,000) by (1 - tax) (in this case, by 1 - 0.2042 = 0.7958).
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  3. #3
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    Re: percentages - taxing problem

    Emakarov, Thank you! A simple solution to a constantly recurring conundrum with billing, I'll pin this on my board so I don't forget again.
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