Question

Nerys checks her tax bill from last year

the tax rates were as follows:
•No tax on the first £11,000 of earnings
•Earnings in excess of £11,000 and up to £43,000 taxed at a rate of 20%
•Earnings in excess of £43,000 and up to £ 150,000 taxed at a rate of 40%
•Earnings over £150,000 taxed at a rate of 45%
Last year Nerys earned £162,700 before tax.
how much tax did she pay in total?

Answer 1

£54,915

Explanation:

The tax table is applied as follows:

first 11,000 -- no tax

11,000 to 43,000 -- tax is 0.20 × (43,000 -11,000) = 6,400

43,000 to 150,000 -- tax is 0.40 × (150,000 -43,000) = 42,800

150,000 to 162,700 -- tax is 0.45 × (162,700 -150,000) = 5,715

Then the total tax on earnings of £162,700 is ...

£6,400 +42,800 +5,715 = £54,915

Nerys paid a tax of £54,915.

_____

Additional comment

The tax computation could be simplified to ...

f(x) = max(0, 0.2x -2200, 0.4x -10800, 0.45x -18300)

In this instance, the value 0.45x -18300 is the highest, at £54,915. Not all the computations are required if you realize the lines cross at x = 11,000, 43,000, and 150,000.