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Calculate Gross Tax only knowing Net Earnings

  1. Nov 19, 2006 #1
    Hi All,

    I was wondering if it is possible to work out a formula for calculating what your gross earnings would have to be to earn a certain net value.

    The tax on earnings scales go like this:

    Between $0 - $6000 you pay no tax.
    Between $6001 - $25000 you pay 15c per dollar.
    Between $25001 - $75000 you pay 30c per dollar.
    Between $75001 - $150000 you pay 40c per dollar.
    Greater than $150000 you pay 45c per dollar.

    So Gross - Tax = Net. Based on the above I'd like to be able to solve what your gross would be if you knew your net earnings.

    Does anyone know how to write the formula for this? I'm having trouble just writing a formula to explain the above solving for gross.

  2. jcsd
  3. Nov 19, 2006 #2


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    Science Advisor

    Just as your tax table is a "step function", so the formula giving gross income as a function of net income will be a step function:
    Let N= net income, G= gross income in dollars.

    If 0<= N<= 6000, then G= N
    If 6001<= N<= 29412, Then N= G- .15G= 0.85G so G= N/.85.
    (the upper limit, $29412, is 25000/.85)
    If 29412<= N<= 107143, Then N= G- .30G= 0.70G so G= N/.70.
    (Again, the upper limit, $107143, is 75000/.70)


    By the way, a more realistic tax schedule would be

    Between $0- $6000 you pay no tax.
    Between $6001- $25000 you pay 15c per dollar over $6000
    Between $25001- $75000 you pay 3750 (.15*$25000) plus 30c per dollar 1over $25000
    Between $75001- $150000 you pay $18750 (3750+ .30(50000)) plus 40c per dollar over $75000
    Over $150001, you pay $48750 ($18750+ .40(75000)) plus 45c per dollar over $150001.
  4. Nov 21, 2006 #3


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    If you'd like a formula in Microsoft Excel to this for you...


    where A1 is the cell which contains the Net salarĂ½.
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