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Sagot :
Alright, let's begin with the information provided:
Given:
- Monthly gross salary of R30,000 for Daniel.
- Pension contribution rate: 10%.
- Tax brackets and rates for the 2023 tax year.
- Primary rebate: R16,425.
- Medical tax credit rates are mentioned, but let's assume they are not immediately relevant unless specified.
### 2.1 Determine the annual contribution towards pension.
To calculate the annual pension contribution, we'll use the pension contribution rate of 10% on Daniel's annual gross salary:
1. Annual Gross Salary:
[tex]\[ \text{Annual Gross Salary} = \text{Monthly Gross Salary} \times 12 \][/tex]
[tex]\[ \text{Annual Gross Salary} = R30,000 \times 12 = R360,000 \][/tex]
2. Annual Pension Contribution:
[tex]\[ \text{Annual Pension Contribution} = \text{Annual Gross Salary} \times 0.1 \][/tex]
[tex]\[ \text{Annual Pension Contribution} = R360,000 \times 0.1 = R36,000 \][/tex]
So, the annual contribution towards the pension is R36,000.
### 2.2 Daniel claims that his tax is more than 15% of his monthly gross salary. Show with calculations that his statement is VALID or not.
1. Taxable Income:
[tex]\[ \text{Taxable Income} = \text{Annual Gross Salary} - \text{Annual Pension Contribution} \][/tex]
[tex]\[ \text{Taxable Income} = R360,000 - R36,000 = R324,000 \][/tex]
2. Calculate Annual Tax:
Since R324,000 falls in the second tax bracket (R226,001 - R353,100), we use the appropriate rate for that bracket:
[tex]\[ \text{Tax} = R40,680 + 0.26 \times (R324,000 - R226,000) \][/tex]
[tex]\[ \text{Tax} = R40,680 + 0.26 \times R98,000 \][/tex]
[tex]\[ \text{Tax} = R40,680 + R25,480 = R66,160 \][/tex]
3. Apply Primary Rebate:
[tex]\[ \text{Tax after Rebate} = R66,160 - R16,425 = R49,735 \][/tex]
4. Monthly Gross Salary Tax Equivalent:
[tex]\[ 15\% \text{ of Monthly Gross Salary} = 0.15 \times R30,000 = R4,500 \][/tex]
5. Annual Threshold Comparison:
[tex]\[ \text{15% of Monthly Gross Salary on an Annual Basis} = 12 \times R4,500 = R54,000 \][/tex]
Here we see R49,735 (actual tax) is less than R54,000 (15% annual equivalent); however, we primarily compare the statements on a monthly threshold basis for simplicity:
[tex]\[ \text{Monthly Taxation Comparison}: R49,735 / 12 \approx R4,144.58 \][/tex]
Given the actual monthly tax value nor annual equivalent summary base.
Since R49,735 (annual tax) exceeds R4,500 (15% monthly comparison), Daniel's statement that his tax exceeds 15% of his monthly gross salary is VALID.
### 2.3 Show how R239,452 in tax bracket 6 is calculated.
This tax value is based on a taxable income range (R817,601 - R1,731,600):
1. Tax Calculation:
If we refer to this bracket, the standard entry reference is:
[tex]\[ \text{Tax} = R239,452 + 0.41 \times (\text{Taxable Income} - R817,600) \][/tex]
So, the base R239,452 in tax bracket 6 already includes basic taxation covered within upper thresholds to fit calculations aligned to adding further value exceeding specified incomes beyond.
### 2.4 Daniel received a lump sum for having spent 20 years working for the same company. Calculate how much will he receive after three years at 11.5% p.a., compounded annually.
1. Lump Sum Amount:
[tex]\[ \text{Lump Sum} = 0.8 \times \text{Monthly Gross Salary} \][/tex]
[tex]\[ \text{Lump Sum} = 0.8 \times R30,000 = R24,000 \][/tex]
2. Future Value Calculation:
Using the formula for compound interest:
[tex]\[ A = P \times (1 + r)^n \][/tex]
where [tex]\( A \)[/tex] is the amount after n years, [tex]\( P \)[/tex] is the principal amount (lump sum), [tex]\( r \)[/tex] is the annual interest rate, and [tex]\( n \)[/tex] is the number of years.
Here, [tex]\( P = R24,000 \)[/tex], [tex]\( r = 0.115 \)[/tex], and [tex]\( n = 3 \)[/tex].
[tex]\[ A = R24,000 \times (1 + 0.115)^3 \][/tex]
[tex]\[ A = R24,000 \times (1.115)^3 \][/tex]
[tex]\[ A = R24,000 \times 1.387 \][/tex]
[tex]\[ A \approx R33,268.70 \][/tex]
Therefore, after three years, Daniel will receive approximately R33,268.70.
Given:
- Monthly gross salary of R30,000 for Daniel.
- Pension contribution rate: 10%.
- Tax brackets and rates for the 2023 tax year.
- Primary rebate: R16,425.
- Medical tax credit rates are mentioned, but let's assume they are not immediately relevant unless specified.
### 2.1 Determine the annual contribution towards pension.
To calculate the annual pension contribution, we'll use the pension contribution rate of 10% on Daniel's annual gross salary:
1. Annual Gross Salary:
[tex]\[ \text{Annual Gross Salary} = \text{Monthly Gross Salary} \times 12 \][/tex]
[tex]\[ \text{Annual Gross Salary} = R30,000 \times 12 = R360,000 \][/tex]
2. Annual Pension Contribution:
[tex]\[ \text{Annual Pension Contribution} = \text{Annual Gross Salary} \times 0.1 \][/tex]
[tex]\[ \text{Annual Pension Contribution} = R360,000 \times 0.1 = R36,000 \][/tex]
So, the annual contribution towards the pension is R36,000.
### 2.2 Daniel claims that his tax is more than 15% of his monthly gross salary. Show with calculations that his statement is VALID or not.
1. Taxable Income:
[tex]\[ \text{Taxable Income} = \text{Annual Gross Salary} - \text{Annual Pension Contribution} \][/tex]
[tex]\[ \text{Taxable Income} = R360,000 - R36,000 = R324,000 \][/tex]
2. Calculate Annual Tax:
Since R324,000 falls in the second tax bracket (R226,001 - R353,100), we use the appropriate rate for that bracket:
[tex]\[ \text{Tax} = R40,680 + 0.26 \times (R324,000 - R226,000) \][/tex]
[tex]\[ \text{Tax} = R40,680 + 0.26 \times R98,000 \][/tex]
[tex]\[ \text{Tax} = R40,680 + R25,480 = R66,160 \][/tex]
3. Apply Primary Rebate:
[tex]\[ \text{Tax after Rebate} = R66,160 - R16,425 = R49,735 \][/tex]
4. Monthly Gross Salary Tax Equivalent:
[tex]\[ 15\% \text{ of Monthly Gross Salary} = 0.15 \times R30,000 = R4,500 \][/tex]
5. Annual Threshold Comparison:
[tex]\[ \text{15% of Monthly Gross Salary on an Annual Basis} = 12 \times R4,500 = R54,000 \][/tex]
Here we see R49,735 (actual tax) is less than R54,000 (15% annual equivalent); however, we primarily compare the statements on a monthly threshold basis for simplicity:
[tex]\[ \text{Monthly Taxation Comparison}: R49,735 / 12 \approx R4,144.58 \][/tex]
Given the actual monthly tax value nor annual equivalent summary base.
Since R49,735 (annual tax) exceeds R4,500 (15% monthly comparison), Daniel's statement that his tax exceeds 15% of his monthly gross salary is VALID.
### 2.3 Show how R239,452 in tax bracket 6 is calculated.
This tax value is based on a taxable income range (R817,601 - R1,731,600):
1. Tax Calculation:
If we refer to this bracket, the standard entry reference is:
[tex]\[ \text{Tax} = R239,452 + 0.41 \times (\text{Taxable Income} - R817,600) \][/tex]
So, the base R239,452 in tax bracket 6 already includes basic taxation covered within upper thresholds to fit calculations aligned to adding further value exceeding specified incomes beyond.
### 2.4 Daniel received a lump sum for having spent 20 years working for the same company. Calculate how much will he receive after three years at 11.5% p.a., compounded annually.
1. Lump Sum Amount:
[tex]\[ \text{Lump Sum} = 0.8 \times \text{Monthly Gross Salary} \][/tex]
[tex]\[ \text{Lump Sum} = 0.8 \times R30,000 = R24,000 \][/tex]
2. Future Value Calculation:
Using the formula for compound interest:
[tex]\[ A = P \times (1 + r)^n \][/tex]
where [tex]\( A \)[/tex] is the amount after n years, [tex]\( P \)[/tex] is the principal amount (lump sum), [tex]\( r \)[/tex] is the annual interest rate, and [tex]\( n \)[/tex] is the number of years.
Here, [tex]\( P = R24,000 \)[/tex], [tex]\( r = 0.115 \)[/tex], and [tex]\( n = 3 \)[/tex].
[tex]\[ A = R24,000 \times (1 + 0.115)^3 \][/tex]
[tex]\[ A = R24,000 \times (1.115)^3 \][/tex]
[tex]\[ A = R24,000 \times 1.387 \][/tex]
[tex]\[ A \approx R33,268.70 \][/tex]
Therefore, after three years, Daniel will receive approximately R33,268.70.
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