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Calculating net pay using cut off rates and tax credits. Calculating gross pay given tax information.

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rebel

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rebelmaths

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{standard}% => $\\frac{\\var{standard}}{100}$

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{higher}% => $\\frac{\\var{higher}}{100}$

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Calculate the gross income tax for the week first as follows:

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Calculate the standard cut-off point amount first by $\\frac{\\var{standard}}{100} \\times \\var{cut}$

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Then, the income tax at the higher rate by $\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut})$

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Finally, add them to get the gross income tax

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$(\\frac{\\var{standard}}{100} \\times \\var{cut}) + (\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut}))$

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Using the gross income tax calculated in above

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Subtract the tax credit, $\\var{credit}$, giving the amount of income tax paid.

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$(\\frac{\\var{standard}}{100} \\times \\var{cut}) + (\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut})) - \\var{credit} = \\var{ans}$

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Look at this website for worked examples:

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how to work out my tax

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Calculate the amount of income tax he pays each week.

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€[[0]]

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$\\var{name}$ pays tax at $\\var{standard}$% on the first $\\var{cut}$ of his money, so you need to find $\\var{standard}$% of $\\var{cut}$.

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He pays tax at $\\var{higher}$% on everything above $\\var{cut}$, so you need to find out how much he earns above the cut off $\\var{cut}$ and get $\\var{higher}$% of that.

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Add the two tax bills together to find the gross tax that $\\var{name}$ owes.

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Subtract his tax credits from this.

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The result is the net tax that he has to pay.

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$\\var{name}$ has a weekly wage of €$\\var{wage}$. His standard cut-off point is €$\\var{cut}$, and his tax credit is €$\\var{credit}$ per week. The standard rate of income tax is $\\var{standard}$% and the higher rate is $\\var{higher}$%.

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Net Tax

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rebelmaths

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{standard}% => $\\frac{\\var{standard}}{100}$

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{higher}% => $\\frac{\\var{higher}}{100}$

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Calculate the gross income tax for the week first as follows:

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Calculate the standard cut-off point amount first by $\\frac{\\var{standard}}{100} \\times \\var{cut}$

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Then, the income tax at the higher rate by $\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut})$

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Finally, add them to get the gross income tax

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$(\\frac{\\var{standard}}{100} \\times \\var{cut}) + (\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut}))$

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Using the gross income tax calculated in above

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Subtract the tax credit, $\\var{credit}$, giving the amount of income tax paid.

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$(\\frac{\\var{standard}}{100} \\times \\var{cut}) + (\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut})) - \\var{credit} = \\var{ans}$

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Calculate the amount of income tax she pays for the year.

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To the nearest euro!!

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€[[0]]

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$\\var{name}$ pays tax at $\\var{standard}$% on the first $\\var{cut}$ of her money, so you need to find $\\var{standard}$% of $\\var{cut}$.

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She pays tax at $\\var{higher}$% on everything above $\\var{cut}$, so you need to find out how much she earns above the cut off $\\var{cut}$ and get $\\var{higher}$% of that.

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Add the two tax bills together to find the gross tax that $\\var{name}$ owes.

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Subtract her tax credits from this.

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The result is the net tax that she has to pay.

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$\\var{name}$ has an annual salary of €$\\var{wage}$. Her standard cut-off point is €$\\var{cut}$, and her tax credit is €$\\var{credit}$. The standard rate of income tax is $\\var{standard}$% and the higher rate is $\\var{higher}$%.

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Net Tax

\n

rebelmaths

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First, calculate the gross income tax; $€\\var{credit} + €\\var{tax}$

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Then to find the standard rate of income tax, as a percentage, divide by the salary and multiply by 100.

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To summarise:

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$(\\var{credit} + \\var{tax}) \\div \\frac{\\var{salary}}{100}$

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Or

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$(\\var{credit} + \\var{tax}) \\times\\frac{100}{\\var{salary}} = \\var{ans}$%

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$\\var{name}$ has an annual salary of €$\\var{salary}$. His tax credit is €$\\var{credit}$, and he pays income tax on all his income at the standard rate of $x$%. If he pays €$\\var{tax}$ in income tax for the year, find the standard rate ($x$%).

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[[0]]%

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Usually we calculate net tax = gross tax - credits.

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For this question we need to turn that around.

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net tax + credits = gross tax.

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What percentage of his income is the gross tax?

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Solve the following to 1 decimal place:

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Income tax

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rebelmaths

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First calculate gross income tax

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gross income tax = income tax + tax credit

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Then, divide by standard rate of income tax, $\\var{standard}$% (or multiply by $\\frac{100}{\\var{standard}})$

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$(€\\var{tax} + €\\var{credit}) \\times (\\frac{100}{\\var{standard}}) = €\\var{ans}$

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A $\\var{job}$ has a tax credit of €$\\var{credit}$ per week and pays income tax on all his wages at the standard rate of income tax of $\\var{standard}$%. If he pays €$\\var{tax}$ in tax per week, find his gross weekly wage, to the nearest cent.

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€[[0]]

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First find the gross tax (as in the previous question).

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This is $\\var{standard}$ % of his total wages. First find 1% of his wages and then multiply by 100 to find his total wages.

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Calculate gross weekly wage

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Gross wage, tax

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rebelmaths

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First calculate the gross income tax:

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standard rate:

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$\\var{cut} \\times (\\frac{\\var{standard}}{100})$

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higher rate:

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$(\\var{salary}-\\var{cut}) \\times (\\frac{\\var{higher}}{100})$

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gross income tax = standard rate + higher rate

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Then remember,

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income tax =  gross income tax - tax credit

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=> tax credit = gross income tax - income tax

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or mathematically:

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$((\\var{cut} \\times \\frac{\\var{standard}}{100}) +((\\var{salary}-\\var{cut}) \\times \\frac{\\var{higher}}{100})) - \\var{tax} = €\\var{ans}$

", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "

$\\var{name}$ has an annual salary of €$\\var{salary}$ and her standard cut-off point is €$\\var{cut}$. The standard rate of income tax is $\\var{standard}$% and the higher rate is $\\var{higher}$%. If she pays €$\\var{tax}$ in income tax for the year, calculate her tax credit.

\n

€[[0]]

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First calculate the gross income tax:

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standard rate:

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x * ({standard}/100)

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higher rate:

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y * ({higher}/100)

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gross income tax = standard rate + higher rate

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Then remember,

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income tax =  gross income tax - tax credit

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First consider the first $\\var{cut}$ euro of her income. Calculate $\\var{standard}$% of $\\var{cut}$.

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Find how much money is taxed at the higher rate and find $\\var{higher}$% of this.

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Now you can find her gross tax.

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gross tax - credit = net tax. If we move this around we get credit = gross tax - net tax

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Calculate to the nearest euro:

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Tax credits

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rebelmaths

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Calculate the gross income by; 

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tax credit + income tax

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then, divide it by $\\var{standard}$% (or multiply by $\\frac{100}{\\var{standard}}$)

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$(\\var{tax}+\\var{credit}) \\times \\frac{100}{\\var{standard}} = €\\var{ansone}$

\n

Note this question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.

\n

 

", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "

Calculate her gross salary for the year, to the nearest cent.

\n

€[[0]]

\n

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Use what you learned in Question 4.

\n

Note this question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.

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\n

$\\var{name}$ paid €$\\var{tax}$ in income tax for the year. Her tax credits amount to €$\\var{credit}$ and she paid income tax on all of her salary at the standard rate of income tax of $\\var{standard}$%.

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rebelmaths

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Part1:

\n

$\\var{tax} + \\var{credit} = €\\var{ans1}$

\n

\n

Part 2:

\n

$€\\var{28000} \\times \\frac{100}{\\var{standard}} = €\\var{ans2}$

\n

\n

Part 3:

\n

Calculate the gross income by; 

\n

$(((\\var{tax}+\\var{credit})-(\\var{cut} \\times \\frac{\\var{standard}}{100})) \\times \\frac{100}{\\var{higher}})+\\var{cut} = €\\var{ans3}$

\n

 

\n

\n

 

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Her gross income tax for the year.

\n

€[[0]]

\n

\n

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Calculate his gross tax as before.

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Calculate how much income tax she paid at the standard rate.

\n

€[[0]]

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She paid income tax at the standard rate on all money earned up to the standard rate cut off point.

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Calculate her gross income for the year:

\n

€[[0]]

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We know how much her gross tax was. In part b we calculated how much of that came from her standard rate earnings. How much of her tax bill came from the higher rate earnings? So how much did she earn at the higher rate?

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\n

$\\var{name}$ paid €$\\var{tax}$ in income tax for the year and her tax credits amount to €$\\var{credit}$. Her standard cut-off point was $€\\var{cut}$. The standard rate of income tax is $\\var{standard}$% and the higher rate is $\\var{higher}$%.

\n

Solve the following to the nearest cent!!

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rebelmaths

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Calculate the gross income by; 

\n

$(((\\var{tax}+\\var{credit})-(\\var{cut} \\times \\frac{\\var{standard}}{100})) \\times \\frac{100}{\\var{higher}})+\\var{cut} = €\\var{anstwo}$

\n

 

\n

\n

 

", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "

Calculate his gross salary for the year, to the nearest cent.

\n

€[[0]]

\n

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Calculate his gross tax as before.

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\n

$\\var{name}$ paid €$\\var{tax}$ in income tax for the year. He has a tax credit of €$\\var{credit}$ and his standard cut-off point was $€\\var{cut}$. The standard rate of income tax was $\\var{standard}$% and the higher rate was $\\var{higher}$%.

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rebelmaths

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