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2.1 According to the SARS data for December 2017, South Africa's 148 266 millionaires earn between R1 million and R2 million per annum - NSC Mathematical Literacy - Question 2 - 2019 - Paper 2
Question 2
2.1 According to the SARS data for December 2017, South Africa's 148 266 millionaires earn between R1 million and R2 million per annum. The number of millionaires i... show full transcript
Worked Solution & Example Answer:2.1 According to the SARS data for December 2017, South Africa's 148 266 millionaires earn between R1 million and R2 million per annum - NSC Mathematical Literacy - Question 2 - 2019 - Paper 2
Step 1
It was stated that the mean monthly income per millionaire is exactly R161 000. Verify, with calculations, whether this statement is CORRECT.
Answer
To verify this statement, we need to calculate the mean monthly income per millionaire. The total annual income for the millionaires is R287,24 billion, which can be converted to rand:
Total annual income = R287,240,000,000
Now, divide this by the total number of millionaires: Mean income per millionaire = R287,240,000,000 / 148,266 = R1,937,328.55
Calculating the monthly income: Monthly income per millionaire = R1,937,328.55 / 12 = R161,444.00
Thus, the statement is INCORRECT as R161,000 is not equal to R161,444.00.
Step 2
Calculate the number of millionaires in South Africa in the previous year (2016).
Answer
The increase in the number of millionaires was 5,006% from the previous year. Let 'x' be the number of millionaires in 2016. Then:
148,266 = x + (5,006/100 * x)
This simplifies to: 148,266 = x(1 + 50.06) = x * 51.06
Now solving for x:
x = 148,266 / 51.06 = 2,901.24
Thus, the approximate number of millionaires in 2016 was around 2,901.
Step 3
Calculate John's total medical scheme tax rebate for the year.
Answer
John's total medical scheme tax rebate for the year is calculated as follows:
First, determine the medical scheme contributions:
Medical scheme rebate for the year = R310 * 2 = R620 (for the primary taxpayer)
For the following beneficiaries (being wife + himself):
= R310 * 2 = R620
Total rebate for the year = R620 + R620 = R1,240.
Step 4
Hence, calculate the amount of income tax he had to pay for the 2018/2019 tax year.
Answer
The amount of income tax John had to pay is found by subtracting the medical scheme tax rebate from his taxable income. Hence:
Total Taxable Income = R2,063,364 Medical Scheme Rebate = R1,240
Income Tax Payable = R2,063,364 - R1,240 = R2,062,124.
Step 5
Calculate, in rand, Megan's annual gross salary using the following exchange rates: 1 euro = 15,64 South African rands and 1 euro = 7,47 Danish kroner.
Answer
Megan's gross annual salary in Danish kroner is Kr600,000. First, we convert this to euros:
Salary in euros = 600,000 Kr / 7.47 = €80,321.28
Now, convert it to rand:
Salary in rand = €80,321.28 * 15.64 = R1,256,224.90.
Step 6
John stated that Megan's total annual deductions (excluding tax) are more than 52% of her annual gross salary. Verify, showing ALL calculations, whether this statement is valid.
Answer
Total deductions are:
Investment policy = Kr229,760 Basic market contribution = Kr48,000 Employment deduction = Kr37,200
Total deductions in kronor = Kr229,760 + Kr48,000 + Kr37,200 = Kr314,960
Now, converting total deductions to rand:
Total deductions in rand = Kr314,960 * (15.64 / 7.47) = R642,163.32
To verify the percentage:
Percentage = (R642,163.32 / R1,256,224.90) * 100 = 51.1% (approximately)
Thus, the statement is INCORRECT since it is not more than 52%.
Step 7
Name the country that has the biggest range between 2019 and the past top marginal tax rates.
Answer
Going through the data in ANNEXURE D, we identify the country with the greatest difference in tax rates between the two years. As per the table, the country with the biggest range is the United States of America.
Step 8
Determine, to THREE decimal places, the probability of randomly selecting one of the G20 countries where the latest tax rates changed from the previous tax rate.
Answer
The probability can be expressed as:
P = rac{ ext{number of countries with changed rates}}{ ext{total number of G20 countries}}
= rac{2}{20} = 0.100.
This is the probability rounded to three decimal places.
Step 9
Step 10
The interquartile range is given as 12. Verify, showing all calculations, whether the given interquartile range is CORRECT.
Answer
To verify the interquartile range, we first need to calculate the first and third quartiles (Q1 and Q3) and then find their difference:
IQR = Q3 - Q1
If Q3 - Q1 equals 12, then the given interquartile range is CORRECT. A detailed calculation based on the data from ANNEXURE D is required.