# Anyone good at maths?

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eleventhirtytwo
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17 Dec 2015, 6:36 pm

Say you need to earn £1000 to cover your monthly expenses, excluding tax.

You pay tax at a flat rate of 20%.

To offset a flat rate of tax of 20% you have to increase your needed earnings by 25% (1250 * 0.8 = 1000).

How would you work out the needed multiplier to offset the tax (25%) without using trial and error (as I did)? Is there an equation?

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eleventhirtytwo
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17 Dec 2015, 6:55 pm

Ah, I'm not thinking tonight. Original number/New number = Percentage change from original.

Sooo...

Tax Offset Multiplier = Needed Salary After Tax / (Needed Salary After Tax * (1 - Tax Rate))

Needed Salary Before Tax = Needed Salary After Tax * Tax Offset Multiplier

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thesewalls
Tufted Titmouse

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25 Dec 2015, 10:59 pm

Just take the reciprocal of the percent you have left after taxes. You have 80%, or .8 of your money after taxes. The reciprocal is 1.25, which is the multiplier for how much more you need to make to offset the taxes.

naturalplastic
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26 Dec 2015, 3:43 am

Been a long time since I took algebra, but I think that you would set it up this way. X is the unknown quantity you are looking for (how much you have to earn before taxes).

X- (20 percent of X)= 1,000 pounds

++++++++++++++++++++++++++++++++++++++++++++++
Then you convert "20 percent" into "two tenths"

X- (.2 X)= 1000

then do this.

.8 X= 1000

Then multiply both sides of the equation by the reciprocal of "point eight" ( which is "one point 25").

X=1,250

^And that's your answer: that you need to take in 1250 a month to clear 1000 each month.

Sigbold
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26 Dec 2015, 3:48 am

Sorry, but would it not be easier to divide the amount of money you need after paying your taxes trough 80 and then multiple it with 100? Or in other terms x/80*100=earnings needed?

Spiderpig
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26 Dec 2015, 12:30 pm

You see, percentages are a good device for making simple things obscure. No wonder they're so widely liked

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Campin_Cat
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26 Dec 2015, 10:42 pm

Yeah, I would've just done, what you did, in your second post.....

1000 pounds (net income) X 25 percent = 250

250 pounds + 1000 pounds = 1250 (gross income)

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