Grossing up salary

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Banshee

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Oct 7, 2020
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If I have a net salary of 45,000 per annum with a standard rate of tax at 20% and marginal rate at 43% how do I gross these amounts up please?
 
Write the gross salary as "G". Then 20% tax is .20G. That reduces the salary to G- .20G= 0.80G. Now what does this "marginal rate" mean? What is "marginal" about it? It is 43% of what? My guess would be that it is 43% what is left after the standard tax is taken so is 0.43(0.80G). If that is correct, then the net salary is 0.80G- 0.43(0.80G)= 0.80G- 0.344G= 0.456G. (That's a lot of taxes!) Since the net salary is 45,000, that gives 0.456G= 45000. Solve for G by dividing 45000 by 0.456.
 
Your question would be more straight forward if you gave the tax rates for bands of income.
For example, in the UK:
Personal allowance (Up to £12,500) 0%
Basic rate (£12,501 to £50,000) 20%
Higher rate (£50,001 to £150,000) 40%
Additional rate (Over £150,000) 45%
 
Basic rate (34,000) 20%
Balance at 41%
Single and tax credit 3,520
PRSI 2%

What I'm having difficulty with is how to know how to calculate the taxes only having the net amount of 45,000.
Thanks.
 
If I understand this tax system correctly

Net pay = Gross pay
less Gross x .02 (PRSI)
less 34000 x .2 (Basic rate)
less (Gross - 34000) x .41
plus 3520 (tax credit)

45000 = G - (G x .02) - (34000 x .2) - ((G - 34000) x .41) + 3520
45000 = G - (G x .02) - 6800 - (G x .41) + 13940 + 3520
45000 = (G x .57) + 10660
Gross pay = 34340 / .57 = 60245.61
 
Thanks.
Can I ask how was the .57 calculated in the third line of the second paragraph please?
 
45000 = G - (G x .02) - 6800 - (G x .41) + 13940 + 3520

45000 = G*(1 - 0.02 - 0.41) - 6800 + 13940 + 3520
 
It may be an obvious question but I just want to be sure I understand so I can solve similar in the future, does the 1 come from G being 100% and included within both brackets? Thanks.
 
G=1G or Gx1

So G - (G x .02) - (G x .41) = Gx1 - (G x .02) - (G x .41) = G( 1 -.02 - .41)
 
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