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Difficulty: HardTypes and Systems of Taxation

The table below outlines a country's progressive personal income tax brackets:

Income BracketMarginal Tax Rate
First N100,000\text{N}100,0005%5\%
Next N200,000\text{N}200,000 (N100,001−N300,000\text{N}100,001 - \text{N}300,000)10%10\%
Next N300,000\text{N}300,000 (N300,001−N600,000\text{N}300,001 - \text{N}600,000)15%15\%
Above N600,000\text{N}600,00020%20\%

If a taxpayer earns a total gross taxable income of N500,000\text{N}500,000 in a year, what is their effective (average) tax rate?

  1. 11.0%11.0\%Answer
  2. B
    15.0%15.0\%
  3. C
    14.0%14.0\%
  4. D
    10.0%10.0\%

Answer

The effective (average) tax rate is 11.0%11.0\%.
Under a graduated progressive tax schedule, tax liability is computed segment by segment. For an income of N500,000\text{N}500,000, tax on the first N100,000\text{N}100,000 is N5,000\text{N}5,000 (5%5\%), on the next N200,000\text{N}200,000 is N20,000\text{N}20,000 (10%10\%), and on the remaining N200,000\text{N}200,000 is N30,000\text{N}30,000 (15%15\%). Adding these amounts gives a total tax liability of N55,000\text{N}55,000. Dividing this total tax liability by total income yields an effective average tax rate of N55,000N500,000×100%=11.0%\frac{\text{N}55,000}{\text{N}500,000} \times 100\% = 11.0\%.

Step-by-Step Solution

1
Calculate the tax payable in the first bracket
N100,000×0.05=N5,000\text{N}100,000 \times 0.05 = \text{N}5,000
The first N100,000\text{N}100,000 of income is taxed at the 5%5\% rate.
2
Calculate the tax payable in the second bracket
N200,000×0.10=N20,000\text{N}200,000 \times 0.10 = \text{N}20,000
The next N200,000\text{N}200,000 of income (from N100,001\text{N}100,001 to N300,000\text{N}300,000) is taxed at 10%10\%.
3
Calculate the tax payable in the third bracket for the remaining income
(N500,000−N300,000)×0.15=N200,000×0.15=N30,000(\text{N}500,000 - \text{N}300,000) \times 0.15 = \text{N}200,000 \times 0.15 = \text{N}30,000
Only N200,000\text{N}200,000 of income falls into the third bracket, taxed at 15%15\%.
4
Sum total tax liability and compute the average tax rate
Total Tax = N5,000+N20,000+N30,000=N55,000\text{N}5,000 + \text{N}20,000 + \text{N}30,000 = \text{N}55,000; Average Rate = (N55,000/N500,000)×100%=11.0%(\text{N}55,000 / \text{N}500,000) \times 100\% = 11.0\%
Average tax rate is defined as total tax paid divided by total gross taxable income.

Key Concept

Distinction between Marginal Tax Rate and Average (Effective) Tax Rate in a Progressive Tax System
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Topics

Types and Systems of Taxation

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