Percentages

[cupboardie]

For example, I am paid �184.70, and I know that my tax rate is 22%.

Without knowing the pre tax amount, how do I work it out using just those figures, �184.70 and 22%?

I have looked on answerbank and a maths forum, but no luck so I hope a brainbox out there can help me!

[Hammer]

Your pay after tax is �184.70.

So 78% (100-22) of your pay is �184.70

Divide by 78 to get 1% of your pay (184.70 / 78 = �2.37)

Then multiply by 100 (�2.37 x 100 = �236.79)

[Ethel]

I am not a brainbox so can't give you the formulae.

I do know that you can't simply 22% from �184.70

However, in the example you give, the pre tax figure is �151.39 and the tax is �33.31.

If you don't need to know the formula, use this site for your calculations. Just change the 17.5 to 22.

http://www.crazysquirrel.com/finance/vat-calcu lator.jspx

[cupboardie]

thankyou thankyou thankyou! i knew i'd learned it at school and it was driving me mad trying to work it out!

[Ethel]

Surely hammer is wrong (apart from the obvious mistake)?

Paying 22% income tax does not mean that 78% of the whole is the pre-tax amount.

That would just give 22% of the whole amount, which is higher.

22% of 100 is 22. Leaving 78.

But 22% of 78 is 17.16, totalling 95.16.

81.97 plus 22% = 100. That makes 18.

(Numbers rounded up/down).


So if the take home pay was �100, the net pay would be �81.97, and tax �18.03.

I can't remember the formula, unfortunately.

[Ethel]

The formula is simple.

Divide the amount by 1.22

That gives the pre - tax amount. :)

[Loosehead]

Hammer is correct. 184.7 is 78% ie G x 0.78 = 184.7 rearranging the equation in school taught fashion we get

G = 184.7/0.78 = 236.79

[dzug]

Regardless of the correctness or otherwise of the arithmetic above, there is an error in the assumption. Your marginal tax rate may be 22%, but you only pay this on part of your income - you will get a proportion of your annual personal tax allowance and a proportion of your annual 10% tax allowance before you start paying 22%.

So as an arithmetical exercise, fine - in the real world no.

[Hammer]

Ethel, you're reading the question wrong. Cupboardie knows the take-home pay, but not the pre-tax amount. Hence take-home pay is 78% of the total pay.

If you don't believe my sums, start from gross pay of �236.79 and then take 22% off ;-)