Mathematical Literacy FINANCE
Mathematical Literacy FINANCE
Mathematical Literacy FINANCE
LITERACY
Grade 12
BOOKLET 1A
FINANCE
TABLE OF CONTENTS
1
Page
3. Topic: Finance 6
3.1.1 Tariffs 8
3.1.2 Tax 17
3.2.1 Tariffs 70
3.2.2 Tax 73
6. Reference 92
7. Acknowledgements 93
2
1. Introduction
The declaration of COVID-19 as a global pandemic by the World Health Organisation led to the disruption of effective
teaching and learning in many schools in South Africa. The majority of learners in various grades spent less time in
class due to the phased-in approach and rotational/ alternate attendance system that was implemented by various
provinces. Consequently, the majority of schools were not able to complete all the relevant content designed for
specific grades in accordance with the Curriculum and Assessment Policy Statements in most subjects.
As part of mitigating against the impact of COVID-19 on the current Grade 12, the Department of Basic Education
(DBE) worked in collaboration with subject specialists from various Provincial Education Departments (PEDs)
developed this Self-Study Guide. The Study Guide covers those topics, skills and concepts that are located in Grade
12, that are critical to lay the foundation for Grade 12. The main aim is to close the pre-existing content gaps in
order to strengthen the mastery of subject knowledge in Grade 12. More importantly, the Study Guide will engender
the attitudes in the learners to learning independently while mastering the core cross-cutting concepts.
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2. How to use this Self-Study Guide.
• This study guide covers selected sections of Finance which form part of paper 1.
• The topic is drawn from the CAPS Grade 10 – 12 Curriculum. Selected sections are presented in the following
way:
o What you should know at the end of the section.
o Explanation of key concepts.
o Summary/Notes.
o Worked examples.
o Practice questions.
o Solutions to practice questions.
• Mathematical Literacy is a highly contextualised subject. Whilst every effort has been taken to ensure that
skills and concepts you will be examined on are covered in this study guide, it is in fact the context used in the
examination that will determine how these skills and concepts are assessed.
• This study guide covers all the cognitive levels.
• Go through the worked examples on your own.
• Do practice examples on your own. Then check your answers.
• Read symbols and explanation table below to understand how marks are allocated.
Symbol Explanation
M Method
M/A Method with accuracy
MCA Method with consistent accuracy
CA Consistent accuracy
A Accuracy
C Conversion
S Simplification
RT/RG/RD Reading from a table/graph/diagram
SF Correct substitution in a formula
O Opinion/Example/Definition/Explanation
P Penalty, e.g. for no units, incorrect rounding off, etc
R Rounding off
NPR No penalty for rounding
NPU No penalty for the units
AO Answer only, if correct, full marks
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3. TOPIC: FINANCE
3.1 Notes/Summaries/Key Concepts
TERMINOLOGY MEANING
Account A record of income and expenditure relating to a particular period or purpose.
Balance This is the difference between debits and credits.
Bank statement The details of all the transactions made from one bank account in a given time period.
Break-even point Break-even point is where the business is at an activity level (doing business) at which total cost =
total sales, i.e. you have made enough income to cover the costs. At the break-even point, you are
making neither a profit nor a loss; from that point on you will be making a profit with each sale (until
new costs are incurred).
Budget A plan of how to spend money. An estimate of income and expenditure.
Bursary A sum of money given to you by an organisation to cover the cost of your formal studies.
Capital Money that is owned by someone and used for the purpose of investing or lending.
Commission The sum of money paid to an agent (usually a salesperson) that is a percentage of the total value of
goods sold by the agent.
Compound interest Interest charged on an amount due, but including interest charges to date.
Consumption rate The rate at which a commodity, such as water, electricity or fuel, is consumed.
Cost-effective Best value for money.
Cost price This is the amount that it costs per unit to either manufacture or purchase an item or to prepare for
a service that will be delivered. This amount is pure cost, no mark-up or profit has been added yet.
Cost rate The price of a product per mass, volume, length or time unit.
Credit This is an entry in an account that shows a payment made into the account.
Credit balance The amount in the account is your own.
Credit card A credit card is a service bank product that allows you to buy goods and pay for them at the end of
the month.
Credit limit The maximum amount you can spend on your credit card.
Debit Money deducted or money flowing out of an account. An entry in an account showing a payment
made from the account.
Debit balance The amount owed to a lender or seller.
Debit order It is an arrangement whereby you give permission to a third party to withdraw money from bank
account on a regular basis.
Deposit A payment made into a bank account.
Disposable income Income that is left over after all payments have been made.
Exchange rate The value of one currency relative to the value of another currency.
Expenditure An amount of money that is spent on something.
Fine print The legal terms and conditions printed on a contract applicable to a transaction or account.
Fixed deposit A single deposit invested for a fixed period at a fixed interest rate.
Fixed expenses These are amounts that must be paid every month and stays the same for a period of time, like
rent, school fees and transport costs.
Fund A source of money.
Gross income The total amount of all an individual’s income before deductions.
Hire purchase Goods and products such as furniture can be purchased using a long- term lease or hire
agreement.
Inflation An increase in the price of a basket of goods or services that is representative of the economy as a
whole.
Interest Money paid regularly at a particular rate for the use or loan of money. It can be paid to you by a
finance organisation or bank (in case of savings); or it may be payable by you to a finance
organisation on money you borrowed from the organisation.
Interest rate value This is the % rate of interest that will be charged on your loan amount, i.e. a percentage value of the
original loan amount.
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Interest value This is the actual rand amount of interest that will be added to your loan.
Investment To put money into an organisation or bank (e.g. by buying shares), so as to gain interest on the
amount at a higher rate.
Investment Something in which you have invested money.
Money invested for a period of time.
Invoice A comprehensive document that details all the work done or items sold, and what costs are due.
Lay-bye It is a form of credit where the buyer pays a deposit and pays the balance in instalments while the
shop keeps the item(s) until it has been paid off.
Loan A loan is an agreed sum of money that is lent by a bank or moneylender (e.g. personal loan or
home loan).
Luxury item or service An item or service that is not essential for daily life, but which makes life easier or more convenient.
Net pay The amount an employee “takes home” after income tax has been deducted.
Overdraft An overdraft is an arrangement you make with the bank that allows you to draw more money than
there is in your account.
PAYE (abbr.) Pay as you earn: tax taken off your earnings by your employer and sent to the South African
Revenue Service before you are paid (the balance).
Remittance slip A piece of paper that accompanies a payment and contains the most important details of the
transaction.
Salary An amount of money paid for the work you do. (This is normally paid monthly.)
Selling price This is the price at which something is offered for sale.
Simple interest Interest charged on the original amount due only, resulting in the same fee every time.
Statement A summary of transactions (debits and credits, or payments and receipts) made on an account.
Tariff The rate charged for a service rendered, e.g. import duties, water consumption cost, etc.
Tax A compulsory levy imposed on citizen’s earnings or purchases to fund the activities of government.
Taxable A service, purchase, income, item or earning that will have tax charged to it.
Tax invoice Printed record of what was bought, what it cost, what was taxable, the tax amount, method of
payment, amount tendered, and change due, if any.
Trillion One-million-million (one followed by twelve zeros).
UIF (abbr.) Unemployment Insurance Fund: A government-run insurance fund which employers and
employees contribute to, so that when employees are retrenched they can collect some earnings (a
portion).
Variable expenses Expenses that change over time or from one week/month to the next. These are things that you
usually pay or buy each month, but the amount changes e.g. telephone and electricity costs.
VAT Value Added Tax (VAT) is a tax that is levied at 15% (currently in South Africa) on most goods and
services, as well as on the importation of goods and services into South Africa.
VAT exclusive price The price before VAT is added.
VAT inclusive price The price after VAT is added.
Wages
Withdrawal Money taken out of a bank account.
Zero rated VAT items These are goods that are exempted from VAT. Groceries that are basic foodstuffs are zero-rated in
South Africa, e.g. brown bread, milk, mielie meal, samp, rice, etc..
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3.1.1 Tariffs
Objectives
Summary
A tariff is the charge in rands per measuring unit for a specific service. Tariffs are not always constant; they
change from time to time.
The formulae for calculating the total cost is:
Total cost = number of units ⨉ tariff (cost per unit)
In this section we are going to deal with the following tariffs:
Municipal
eg electricity, water,
sewage
Tariffs
Transport Telephone
e.g bus, tax, train, parking e.g cell phone, landline
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Electricity tariffs
The table below indicates the example of sliding scales for electricity tariffs
Household
(all tariffs are VAT exclusive) VAT to be charged at 15%
Worked example 1
Solutions
1.1 R0,9440
1.2 Using the table, we can see that the 250kWh is made up of the following:
First 50 kWh = 50 × R0,8375
= R41,875 (no rounding at this stage)
∴ 250kWh – 50kWh = 200kWh
Then 200 = 200 × R0,9440
= R188,80
Total amount = R41,875 + R188,80
= R230,675 (no rounding at this stage)
15
Amount of VAT = × R230,675
100
= R34,60125 (no rounding at this stage)
Total amount to be paid = R230,675 + R34,60125
= R265,27625
» R265,28
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Water tariffs
Water tariff, just like electricity tariffs also varies from one place to the other.
Note:
1 kℓ = 1000ℓ
Ø The amount payable for water also depends on the number of kl of water used during the month.
Ø Water is charged at a sliding scale. The more water you use, the higher the rate at which you
are charged.
The table below indicates the example of sliding scales for water tariffs
Residential (all tariffs are VAT exclusive) VAT to be charged at 15%
Up - 6 kℓ First 6 kℓ Free
> 6 kℓ - 10 kℓ Next 4 kℓ R5,21 per kilolitre
> 10 kℓ - 15 kℓ Next 5 kℓ R7,87 per kilolitre
> 15 kℓ - 20 kℓ Next 5 kℓ R10,52 per kilolitre
> 20 kℓ - 30 kℓ Next 10 kℓ R13,38 per kilolitre
> 30 kℓ – 40 kℓ Next 10 kℓ R13,97 per kilolitre
> 40 kℓ Over 40 kℓ R16,96 per kilolitre
Worked example 2
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Solution
2.1 To accommodate households with low or no income.
2.2 Using the table, we can see that the 21 kℓ is made up of the following:
6 + 4 + 5 + 5 + 1 = 21 kℓ
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Amount of VAT = × R126,17
100
= R18,9255
Total amount = R126,17 + R18,9255
= R145,0955 » R145,10
Telephone tariffs
Cell phone networks uses either prepaid or contract billing structures. Different networks charge
different tariffs. The most common networks in South Africa are:
Ø Vodacom
Ø MTN
Ø Cell C
Ø Telkom
Note:
Units can be in minutes or seconds
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Contract tariff system
A cell phone contract for a specific period is taken out from a service provider.
The cost per month includes:
Ø Subscription fee
Ø Cost for the calls
Contract cost = subscription fee + (total number of minutes – number of free minutes) ⨉ tariff
Worked
example
3
Tshepo came across the following option as he was shopping for a new cell phone.
Solution
= R279,00 + R24,75
= R303,75
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Practice Questions
Question 1
The table below shows the rates for domestic prepaid electricity:
1.1 The George family used 250 kWh of electricity for the month of December. Calculate (3)
the amount they need to pay.
1.2 In January they used 351 kWh. Determine the difference between the December and (5)
January payments.
Question 2
The table below indicates the Mangaung local Residential water tariffs for 2016/2017 and
2017/2018. These tariffs are applicable for both the prepaid and billed accounts. All tariffs are
VAT exclusive.
Mangaung local municipality water tariffs (Residential)
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Question 3
The Department of Correctional Services became aware of a problem that Metro High School was
experiencing with violent incidents at the school. They invited the school to visit one of their prisons
on condition that one teacher had to accompany every group of 10 learners or fewer.
Mr Palm, the principal, must hire a bus to take the learners and teachers to visit the prison.
Graphs representing the total cost of hiring buses from two different companies are drawn below.
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3.1 The total cost for hiring a bus from Company P is calculated by using the following
formula:
Use the graphs above and write down a formula for calculating the total cost
(in rands) for Company Q in the form:
Q.
3.2.2 The ratio of learners to teachers, if the maximum number of passengers is (4)
Question 4
MaNdlovu has a landline telephone. A service provider has offered her a choice of two
different call packages
CALL PACKAGE 1 CALL PACKAGE 2
• First 100 minutes are free • First 500 minutes are free
• Calls cost R0,50 per minute • Calls cost R0,50 per minute
4.1 Write down a formula that can be used to calculate the total cost
(in rands) for CALL PACKAGE 2, in the form:
Total cost (in rands) = … (2)
4.2 Using the formula in 3.2, calculate the total cost (in rands) if MaNdlovu made calls for (4)
a total duration of 510 minutes.
4.3 Determine, with calculations, the call package that will be cost effective for (6)
MaNdlovu if she makes only 300 minutes of calls per month.
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Question 5
The parking ticket of Ntsiki’s mother at Bram Fischer International airport showed the following information:
5.1 Determine the amount that Ntsiki’s mother must expect to pay for using the airport’s shaded (3)
parking.
5.2.1 The circumstances under which a person will feel disadvantaged if the parking ticket is (2)
lost.
5.2.2 The length of time for both the shaded and open parking, that a lost parking ticket (4)
would be an advantage.
5.3 What measures are taken to discourage car owners, who must wait for the passengers, to use the (2)
drop and go parking?
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Tax
Objectives
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In this booklet we are going to deal with the following taxes:
VAT
TAX
INCOME
TAX
INCOME TAX
Income Tax is defined as a compulsory payment to the state, which is deducted from person or
business’ earnings for the state to provide services to its citizens.
This amount is paid to the South African Revenue Services (SARS) and can be deducted from
taxpayer’s salary every month (PAYE)
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VAT
• VAT- exclusive amount : means that 15% VAT must still be added.
• Thus,
VAT VAT
inclusive exclusive
OR OR
233
R529,99 x 224 = $460,86 15
× $460,86 = $69,13
100
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NB! COMMON MISTAKE MADE!!!
The item costs R529,99 (VAT inclusive). Calculate the original price.
VAT inclusive means that VAT was added to the original price.
VAT = R529,99 X 0,15
= R79,50
VAT amount: R529,99 – R79,50 = R450,49 which is incorrect
(This is incorrect as the VAT was not calculated on the final price, but on the original price)
Correct calculation
233
R529 × 224
= R460,00
VAT Exemption: Some products or services may not be taxed. This means that there is
no VAT charge for them otherwise referred to as VAT exempted.
Below is a list of some VAT exempted products and services.
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Working with an invoice
Sixole Municipality
VAT No: 29810784
P. O. Box 5200
The Hage 2443
Account number: 400200321 Date: 04 April 2017
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Worked example 1
Below find a till slip for Sasha ‘s groceries. Study the till slip ans answer the questions that follow:
SHANEY STORES
11TH STR, DOODELVILLE
TEL: 031 454 5765
TAX INVOICE: VAT No. 44223377556644
1.1 Why are some of the items marked with an asterisk (*) ? (2)
1.2 Determine the total cost of the items that are VAT inclusive. (2)
1.3 Show, by means of calculations whether you believe the VAT calculations are correct or (4)
not.
Solutions
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Worked example 2
The cricket coach of a school would like to buy cricket equipments for the school cricket team. The
piece list is shown below
ITEM COST
Helmet R350 each
Gloves R95,50 a pair
Box of 4 cricket balls R170 a box
Cricket pads R135 a pair
Cricket bats size 3 R550 each
Cricket bats size 5 R750 each
2.1 If the coach needs 16 balls, how many boxes of cricket balls woulld he need? (2)
2.2 If the coach orders, 4 helmets; 3 pairs of gloves; 8 of balls; 3 pairs of cricket pads; 2 size 3 (3)
bats and 2 size 5 bats, what will the total cost of the items be?
2.3 Determine the amount of VAT at 15% that will be charged on the order. (2)
2.4 If a handling fee of R100 is charged on the goods bought. How much (incl. VAT) will the (2)
school have to pay in total for this order?
2.5 The annual budget for cricket is R10 800, what percentage of the budget was spent on
equipment for this season? (3)
Solutions
2.1 4 boxes
= R5 031,50
= R754,73
= R5 886,23
2.5 4 556,78
× 100
23 533
= 54,5 %
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Practice Questions
Question 1
Question 2
Question 3
The Easter Show is an annual event held in Cape Town. The Elie family,
consisting of two adults aged 45 and 48, three children aged 5, 6 and 16 and a
grandmother aged 75, planned to visit the Rand Show.
TABLE 1 below shows the duration and ticket prices of the 2017 Easter Show.
TICKET PRICING
DURATION VISITORS PRICES INCLUSIVE
OF
AGE CATEGORY
15% VAT
Adults (aged 17 to 64) R150
Friday 14 April Pensioners (65 years and older) R50
Teens (aged 13 to 16) R50
to Children (aged 6 to 12) R20
Children (under 6) free
18 April to 20 April Adults and pensioners receive a 50% discount
Sunday 23 April
09:00 – 19:00
INCOME TAX
Income Tax is defined as a compulsory payment to the state, which is deducted from person or business’
earnings for the state to provide services to its citizens.
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This amount is paid to the South African Revenue Services (SARS) and can be deducted from taxpayer’s
salary every month (PAYE).
The process of calculating personal income tax can be illustrated as follows:
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GROSS INCOME
The sum of all earnings before any deductions have been made.
PENSION FUND
•Government Employees have GEPF while Private Sector has a Provident Fund.
•7,5% of your basic salary is contributed towards a pension fund and is tax-deductible.
•It should be multiplied by 12 to give the annual contribution.
DONATIONS
* A gift to a person who usually is registered with the authorities under Section 18A.
* The maximum amount allowed for tax deduction is R100 000. u
TAX THRESHOLD
• Persons earning more than the tax threshold are liable to pay tax.
• The income level at which someone needs to pay tax.
• Anyone who earns less than this amount does not have to pay tax.
• This amount is determined by the government every year.
Example: A person who is 60 years old and earns less than R83 100 does not have to pay tax.
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INCOME TAX TABLE
SARS (South African Revenue Services) issues tables to be used when determining tax to be paid by
individuals.
Primary R14 958 R14 220 R14 067 R13 635 R13 500 R13 257 R12 726
Secondary (65 and older) R8 199 R7 794 R7 713 R7 479 R7 407 R7 407 R7 110
Tertiary (75 and older) R2 736 R2 601 R2 574 R2 493 R2 466 R2 466 R2 367
Tax Thresholds
Under 65 R83 100 R79 000 R78 150 R75 750 R75 000 R73 650 R70 700
65 an older R128 650 R122 300 R121 000 R117 300 R116 150 R114 800 R110 200
75 and R143 850 R136 750 R135 300 R131 150 R129 850 R128 500 R123 350
older
https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals
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For persons earning
above the tax
threshold
REBATES
It is the relief individuals who pay tax get according to their age
§ Rebates are fixed amounts deducted (taken off) from your annual tax payable.
§ Everyone qualifies for the PRIMARY rebate.
§ People 65 and over qualify for the PRIMARY and SECONDARY rebates.
§ People 75 and over qualify for the PRIMARY, SECONDARY and TERTIARY
rebates.
§ Rebates are subtracted AFTER you have calculated the annual tax payable.
§ Medical tax rebates are received by the main member (The person who pays the medical aid).
§ This rebate gets deducted AFTER the annual tax payable has been calculated.
§ The medical tax credit allocated for the first dependent equals that of the main member, every member
thereafter has the same different medical tax credit.
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STEPS TO CALCULATE INCOME TAX
STEP 1:
Determine the annual income
Multiply the monthly income by 12
STEP 2:
Determine the tax deductible income.
STEP 3:
Subtract the tax-deductible items e.g. Pension and donations
Taxable income= Annual Income – tax deductible income
STEP 4:
Check if the person qualifies to pay tax by using tax threshold table.
Those earning less than the threshold do NOT have to pay tax.
STEP 5:
Identify the correct tax bracket and write it down.
Substitute the taxable income into the given formula.
Use BODMAS to find the tax for the year.
STEP 6:
Calculate and subtract the rebates
Remember: check the age of the individual to see which rebate(s) they qualify for
STEP 7:
Calculate and subtract the medical tax credits, remember to check the number of
how of dependents.
This value is to be multiplied by 12 for the annual amount.
STEP 8:
To determine the monthly income tax, divide the answer by 12.
ANSWER
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Worked example 1
Consult the Tax Table for indiividuals for 2020/2021 tax year to answer the questions that follow:
(See Annexure)
1.1 Into which bracket does a person who earns a taxable income of R454 563 fall?
Answer: Bracket 4: 105 429 + 36% of taxable income above 445 100
1.2 Which rebate would a 52 year old person receive?
Answer: Primary rebate
1.3 Expain whether a 65 yr old earning 120 000 should pay tax or not.
Answer: No, they earn below the tax threshold.
Worked example 2
Casy is 25 years old and earns a monthly income of R25 000. Using the table below, calculate the amount of
tax payable without considering the rebates.
Solution
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Worked example 3
Bongani is a 35 year old man who earns an annual taxable income of R236 700.
REBATES
Primary rebate Under ager 65 R 14067
Secondary rebate Age 65 to 75 R7713
Tertiary rebake Older than 75 R 2574
2.1 Using the tax table for the 2018/2019 tax year calculate Bongani’s annual tax payable.
Solution
2.1 Step 1: Find the correct tax bracket according to his annual taxable income of R236 700
§ Use the tax bracket to calculate his annual tax payable.
=R 35 253 + (26% of 236 700 – 195 850)
=R 35 253 + (26% x R 40 850)
=R 35 253 + (R 10 621)
= R 45 874
Step 2:Deduct the PRIMARY rebate
= R 45 874 – R 14 067
= R 31 807 is Bongani’s annual tax payable
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Worked example 4
Cally is a 55 year old woman who earns an annual taxable income of R350 000. She pays medical aid
for herself and her daughter. Using the tax table for the 2018/2019 tax year calculate Cally’s monthly tax
payable.
Solution
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Practice Questions
Question 1
All employers have an obligation to provide their employees with a payslip monthly. Use the payslip
provided to answer the questions that follow:
195 851 – 305 850 35 253 + 26% of taxable income above 195 850
305 851 – 423 300 63 853 + 31% of taxable income above 305 850
423 301 – 555 600 100 263 + 36% of taxable income above 423 300
555 601 – 708 310 147 891 + 39% of taxable income above 555 600
708 311 – 1 500 000 207 448 + 41% of taxable income above 708 310
1 500 001 and above 532 041 + 45% of taxable income above 1 500 000
Source: https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals
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Question 2
Precious is a 40 year old temporary worker at ABC trading. She earns R5 500 per month. Use the
table below to answer the questions that follow:
Source: https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals)
2.1 Determine, by means of calculations, whether she qualifies to pay tax. (3)
2.2 Show how the value of R 35 253 in the second tax bracket was calculated . (3)
Question 3
Yamkela, a 64-years-old employee, receives a gross salary of R37 537,50 per month.
• He contributes 7,5% per month towards the Government Employees Pension Fund (GEPF)
which is tax deductible.
• He also donates R575 per month to a charity organisation, the donation is tax deductible.
3.1 Calculate the total amount that Yamkela pays towards the pension fund and donations
for the year. (6)
3.2 Hence, calculate Yamkela’s annual taxable income. (3)
3.3 Verify, with the necessary calculations, that Yamkela’s tax that he pays permonth is more than
R6 850. (7)
3.4 Explain why people who are aged 75 years and older pay less tax than people younger
(2)
than 75 years and earning the same taxable income.
3.5 The monthly gross salary of Yamkela increased by 6,4% in 2019. Calculatewhat his gross
(2)
salary was in 2018.
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Question 4
Pierre (28 years old) started a new job on 1 March 2020 at Expert Systems with a starting salary of
R168 000 per year. His letter of appointment states that he is not entitled to a bonus. Refer to his
incomplete payslip below and the tax table on ANNEXURE A to answer the questions that follow.
Total deductions D
Net salary (R) E
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Question 5
Joy is a 52-year-old nurse who earns a salary of R286 500 per annum. She contributes 7% of her annual
salary to a pension fund. She only has her 2 daughters listed as a dependents on her medical aid. She
is concerned that the R4000 monthly income tax deduction is too much.
ANNEXURE A
Rates of tax for individuals
2021 tax year (1 March 2020 - 28 February 2021)
Taxable income (R) Rates of tax (R)
1 – 205 900 18% of taxable income
205 901 – 321 600 37 062 + 26% of taxable income above 205 900
321 601 – 445 100 67 144 + 31% of taxable income above 321 600
445 101 – 584 200 105 429 + 36% of taxable income above 445 100
584 201 – 744 800 155 505 + 39% of taxable income above 584 200
744 801 – 1 577 300 218 139 + 41% of taxable income above 744 800
1 577 301 and above 559 464 + 45% of taxable income above 1 577 300
Tax Rebate
2020/2021 2019/2020 2018/2019
Primary R14 958 R14 220 R14 067
Secondary (65 and older) R8 199 R7 794 R7 713
Tertiary (75 and older) R2 736 R2 601 R2 574
Tax Thresholds
Age
35
Interest and Hire-purchase
Objectives
SUMMARY
Ø Interest is money paid regularly at a particular rate for the use or loan of money.
• It can be paid to you by a financial organisation or bank (in case of savings); or
• It may be payable by you to a financial organisation on money you borrowed from the
organisation or invested at the organisation.
Ø Interest rate is the percentage used to calculate the amount of interest that is
charged from you or paid to you.
Ø Interest value is the actual rand amount of interest that will be added to your loan or investment.
In this section we are going to deal with the following type of interest:
SIMPLE
INTEREST
COMPOUND
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Simple interest
Ø If we know what the interest rate is, we can calculate the amount of interest quite simply.
\ The amount of interest payable depends on the interest rate.
Ø The lower the interest rate, the lesser the payment and,
Ø The higher the interest rate, the more the payment.
Worked example 1
Jan wants to buy a bicycle. He then borrowed R800 from his uncle and promised to pay it
back in 3 months at a simple interest rate of 5%.
Solutions
1.1 R800
37
Now that we have realised that the principal and interest stays the same, we can do
the above solution this way:
5
Interest = ´ R800
100
=R40
Then total interest = R40 ´ 3
= R120
\ Total to be paid = R800 + R120
= R920
Ø If you are given the final amount, then you follow these steps to find the interest rate:
• Find the difference between the final amount and the original amount, this gives you the
amount of interest.
• Work out what percentage the amount of interest is of the principal amount.
Worked example 2
Jan paid his uncle a total amount R920 after borrowing R800 to buy a bicycle. Determine the
interest rate that was charged.
Solution
Ø Simple interest will always be represented by a straight line graph, where interest
represent a constant increase.
38
Worked example 3
The table below represents simple interest on R800 borrowed at 5% interest over a period of 3
months.
Month Principal Interest Total amount
1 R800 5 R800 + R40
´ R800
100 = R840
=R40
2 R800 5 R840 + R40
´ R800
100 = R880
=R40
3 R800 5 R880 + R40
´ R800
100 = R920
=R40
Solution
940
920
900
Total amount
880
860
840
820
800
1 2 3
Number of years
39
Compound interest
Worked example 4
Jan wants to buy a bicycle. He then borrowed R800 from his uncle and promised to pay it
back in 3 months at a compound interest rate of 5%.
Determine the total amount Jan has to pay.
Solution
Table illustration
Ø It is therefore safe to say that in compound interest, you also earn interest on interest.
40
5
2nd month interest = ´ R840
100
= R42
Total amount = R840 + R42
= R882
= R926,10
Ø In Mathematical Literacy, compound interest is calculated using the step by step method used above.
Worked example 5
The table below represents compound interest on R800 borrowed at 5% interest over a period
of 3 months.
41
Solution
1400
1300
1200
Total amount
1100
1000
900
800
1 2 3 4 5 6 7 8 9 10
Number of years
Ø Daily
Ø Monthly
Ø Quarterly
Ø Half yearly
Ø Annually
Ø Most people don't have the cash up front to purchase items such as TVs, fridges, coaches etc., so
they buy them on a hire purchase agreement.
Ø A hire purchase agreement is therefore a financial agreement between the shop and the customer
about how the customer will pay for the desired product.
Ø The interest on a hire purchase loan is always charged at a simple interest rate and only charged
on the amount owing.
Ø Most agreements require that a deposit is paid before the product can be taken by the customer.
Ø The principal amount of the loan is therefore the cash price minus the deposit.
Ø The total loan amount is then divided into monthly payments over the period of the loan.
Ø Payment period is usually 12, 24, 36, 48, 60, and 72 months
42
Worked example 6
Me Tsie decided to buy the following lawn-mower which was advertised as follows:
Deposit: R2 300
Instalments: R975 x 36 months
Solutions
43
Practice Questions
Question 1
Tumi has set aside R800 per month for the last two years. He then decided to invest this money
in a bank in order to put down a deposit to buy a house. Tumi approached a bank that offered
him 12,5 % p.a. simple interest for a period of 36 months.
1.1 Calculate the amount that Tumi will be able to invest in the bank, if he is going to
invest the total amount he has set aside.
(3)
1.2 Determine the interest he will earn from the bank.
(4)
1.3 What is the total amount that he will receive at the end of the investment period?
(2)
Question 2
Tumi managed to find the house of his dreams, the price of the house was R549 000. He then
applied for a home loan at the bank because he did not have the entire amount. Tumi decided
to pay 11,5% deposit.
2.1 Calculate how much Tumi had to put down as a deposit for the house. (2)
2.2 If Tumi uses the money he received from the bank at the end of his investment term,
will he have enough to pay for the deposit? Show by
(3)
means of calculations.
2.3 Tumi learns that he will have to pay a monthly instalment of R5 380 over a period of
20 years.
2.3.1 If the interest rate does not change, Show with calculations that the total
amount paid, including the deposit will be R1 354 335.
(3)
2.3.2 How much more money would Tumi have paid by the end of the
20 years?
(2)
2.3.3 Calculate the percentage interest that Tumi would have paid by the end of 20
years if the monthly instalment did not change.
Round your answer off to one decimal place.
(3)
44
Question 3
Study the advert below and then answer the questions that follow.
Question 4
Mr Moleko has two options for borrowing money:
• His uncle has offered to loan him R16 000 for five years at 18% per annum, simple
interest.
• His bank will offer him a personal loan of R16 000 for five years at 16% compound
interest per annum.
Showing all calculation, determine the option that will be best for Mr Moleko.
(10)
45
Question 5
Mrs. Mhlaba is planning on doing a baking course and therefore decided to buy a food
processor.While browsing the internet, she came across the following special promotion:
Kenwood-Titanium Chef Food Processor
Was: R7 139,99
Special price now: R6 499,00
Mrs. Mhlaba doesn’t have enough cash to pay for the Kenwood – Titanium Chef food
processor.She then decided to buy it on a hire-purchase agreement deal.
The hire-purchase deal entails the following:
• 15% deposit
• 18,5% annual simple interest rate on the remaining balance
• 3 years to repay
46
Summary:
Income and Expenses:
Income is exactly as the word states, money that comes in, while expenses is money
that leaves an account or business.
Income and expense statements allow us to keep track of our finances. This shows
exactly how much money comes into or leaves your business or account.
Fixed and
Variable
Expenses
Profit/Loss
Fixed and Variable
Income
Fixed vs Variable Expenses: Those expenses that do not change are called fixed, while
those who change are called variable.
Eg. Rent or salaries could be fixed for a business while insurance or car instalments
could be fixed for an individual.
Fixed vs variable Income: Fixed income is income that is constant, while variable
income can change monthly.
47
Budget vs Income and Expense Statement
Budget is a list of expected income and expenses while a statement lists the actual income
and expenses.
A quotation can be given for any goods or services to be delivered in the future. A
quotation always has certain conditions which apply and is only valid for a certain period
of time.
An invoice is issued after work has been done/article(s) is/are sold/services were
delivered. The invoice specifies the amount that the consumer has to pay the service
provider.
Worked example 1
Cally is the owner of Cally’s Corner Shop. She pays rent monthly and draws her own salary. She
has three people working for her. One in the deli, one in the bakery and one cleaner. The income
and expenditure statement for Cally’s Corner Shop is shown on the table below. (All values given
are in rand)
48
Use the information on the previous page to answer the questions that follow.
1.1 Show how the total income for March was calculated
1.2 Show how the net profit for February was calculated.
1.3 Calculate the profit made from General sales over the three-month period?
1.4 The property owner has decided to increase rental by 9,8 %. Calculate the new rental
amount for the store each month.
1.5 Cally, the owner of the shop, wants to increase his advertising budget by R300 in May.
Calculate the new total as a percentage of the total expenses for April
1.6 Is the amount of money spent on advertising every month justifiable? Suggest a reason
for your answer.
1.7 Suggest an example of what may be included in ‘Maintenance’ expenses.
1.8 Calculate the percentage increase in profit from February to April
1.9 Which expenses decreased from February to March?
1.10 How can Freddy use this income and expense statement to budget his expenses for
May?
Worked example 2
The following is the income and expenditure statement for Ally’s Boutique for a specific month:
EXPENDITURE INCOME
OPERATING COSTS PRODUCTION COST
Rental R5 000,00 Fabric used R25 000,00 Dresses made R60 000,00
Electricity R450,00 Other R10 000,00
material used
Water R120,00 Fittings R3 850,00
Telephone R900,00 Seamstress E
and internet wage
Total R6470 Total R42 550 Total F
Source: adapted from grade 12 Math Lit revision workbook
49
Solutions
1.1 R9678 + R7854 + R12976 = R30 508
1.2 Profit = R29586 –R23965
= R5621
1.3 GSI: R13450 + R12976 + R 13450 = R39876
Question 2
50
Practice Questions
Question 1
Study Layla’s Delicious Sea Food business budget given below and answer the
questions that follow:
Variable Expenses:
Electricity & water R 8 200
Consumables R 120 000
Total Income: R385 000 Total Expenditure: R327 700
Source: adapted from grade 12 Math Lit revision workbook
1.1 Assist Layla to complete the budget and calculate the profit or loss.
1.2 The business had a profit of R28 000 during the previous year. Layla has a partner with
whom she shares the profit in the ratio 3:1, where the biggest share goes to Layla.
Calculate each partner’s share of the profit of R28 000.
1.3 Their rent for the next year will increase by 7,5%. What will their total rent be for the
following year?
1.4 Calculate the value of A?
1.5 13.5% of their total salaries bill is usually paid to casual delivery personnel. Calculate
the average monthly amount paid out to casual workers.
51
Question 2
The table below shows the summary of Income and Expenses statement with notes of the South
African National Blood Service (SANBS) for the financial year ending 31 March 2016. Some of
the amounts have been omitted.
Use the table and he information above to answer the questions that follow:
2.1 Communication costs decreased by 4,402% from 2015 to 2016. Calculate, to the
nearest thousand rand, the communication costs for 2016.
(4)
2.2 The SANBS expects a 17,5% increase in the costs of its product testing materials and
consumables. Explain what possible impact this could have on their profit for the year.
(2)
2.3 Compare, showing all calculations, the 2015 and 2016 percentage profit for the SANBS.
(5)
Question 3
52
Callan invites Lauren to Shezam Cinema to watch a 3D Movie. The table below shows the
pricelist at the cinema. He decides to go on Friday and buys two large cooldrinks and two boxes
of popcorn.
Shezam Cinema Prices Cooldrink prices
Ticket 2D Movie 3D Movie Small R15 250ml
Normal R50 R75 Medium R20 340ml
Budget R25 R35 Large R25 500ml
Tuesday
Combo deal on Tuesday: 1 popcorn
+ 1 large cooldrink for R40
3.1 If the popcorn costs R15 each. Calculate the total amount that David paid. Use the
formula:
3.3 Which size cooldrink is the most value for money in your opinion? (2)
53
Cost and Selling Price; Break Even Analysis
Cost and
Selling Price
In order for a business to show a profit, the Income needs to exceed the expenses.
For this to happen, the owner needs to know how much to sell the goods for.
For this we need to set up equations that can help us project how the business will perform
54
Finding the Break Even Point
Follow these steps when doing break-even point questions:
Formulate
Draw
Summarise equations
Complete graphs Analyse the
the for Cost
the table using the graph
situation and
table
Income
¶ When you run a small business, you must be able to calculate the number of items
you need to sell in order to make a profit.
¶ Two graphs are drawn on the same grid, the point where these two lines intersect is
called the BREAK-EVEN POINT.
¶ You must be able to read the profit or loss from the graph
VARIABLE COST
source:https://www.freepik.com/free-vector/break-even-point-graph_4489537.htm
55
Break-Even Analysis Model
Application: Skills:
Find the number of units? You must be able to draw a
graph; read information off
Show changes over time the graph, explain what each
Find break even point area means
Break
Even
Analysis:
Break even : when income = expenses
Profit: above break even point
Loss below break even point
Cost per unit= Total Costs divided by no. of items
Worked examples
Example 1
Maddy’s needs to know how her new business is performing. She has set up a
pop-up hamburger stall outside the mall. She has a fixed cost of R500 per month for the stall.
The cost price of the ingredients is R10 per hamburger. She sells the hamburgers for R25
each.
The table below shows her income and expenses for the sale of the hamburgers.
Use the information above, as well as the table to answer the questions that follow:
Solution:
Your first equation will be constructed based on the Total Expenses for the
hamburgers.
• Expenses:
Fixed Cost = R500.00
Variable Cost = R10.00 X no. made (Use N as the variable)
I = R25 x N
56
STEP 2: Using a table
TC = R 500 + (R10 x H)
I = R25 x N
3. Use the Income equation to determine C, the number of hamburgers that are
made.
Income = R25 x N
R1875 = 25 X N
>25?4
Thus N = 74
= 75 Hamburgers
We can now plot these values on a set of axes to give two graphs − one to represent the
income and the other for the total costs.
4. Draw a graph indicating the income and expenses for Maddy’s hamburgers sales.
57
Solution:
1200
1000
Amount in Rands
800
600
400
200
0
0 10 20 30 40 50
No. of hamburgers
Income Expenses
5. Determine what the total cost would be if Maddy sold 45 hamburgers for the month.
6. Calculate the total income if Maddy sold 45 hamburgers.
7. Verify with the necessary calculations that Maddy has made a profit of R175 if he
sold 45 hamburgers a month.
8. Use the graph to determine how many burgers she would have to sell to cover her
expenses?
9. What do we call this point?
Solutions:
Let us consider the school approaching a printing company to lease new photocopier machines.
The invoice below shows the costs involved for three different contracts with a particular
company.
2.1 Provide equations for the cost involved with renting from each of the
companies above.
59
Solution:
Contract 1: Has a Fixed monthly fee and a further 35c per page.
Thus, Costs= R500 + R0.35 X every page copied(P)
Contract 2: Has a fixed charge of R650 per month, but only starts charging for
prints after 500 free pages have been copied.
Thus, Costs = R650 + 25c X (number of pages above 500)
= R650 + 25c X (number of pages copies – 500)
Solution:
Complete a table to analyse the data
In the following example shows the data for various photocopier contracts
5
2
0
3
60
Notice that the table includes 501 and 1001 copies. On contract 2 the page fee only applies for more
than 500 copies (i.e 501 and more). So the cost on this contract will change after 500 copies. A similar
situation happens on contract 3 when there are more than 1000 copies (i.e. 1001 or more)
No look again at the invoice presented by the company. NOTICE how IMPORTANT it is to complete
an analysis of the costs involved before you choose a contract?
Solution:
Camparison of 3 Contracts
Crossing point
1800 for contract 1&3
1600
1400
1200
Cost in Rand
1000
600
400
200
0
0 100 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250
Number of copies
61
2.4 Analyse the graph and provide the school with a recommendation as to which option
would be best.
Now you are ready to make a decision based on the above information
Solution:
Thus if the school makes more than 3500 copies in a month, contract 3 would be cheaper,
even though it is more expensive initially.
However, if the contracy was for home use where between 400 and 3000 copies were made a
month, contract 2 would be best.
62
Practice Questions
Question 1
Tally High School tuckshop sells pears
during lunch to raise funds for a sports tour.
They bought a crate of 250 pears
for R255,00. They sold them at R3.00 each.
Question 2
2.4 Complete the following tables for INCOME and COSTS for Shelley’s business:
Expenses:
No. of Bags 0 1 5 10 20
Costs A 155 B 830 1580
Income:
No. of Bags 0 1 D 10 20
63
2.5 Use the information provided in the tables to draw line graphs for (6)
COSTS and INCOME on the set of axes provided below. Label your graphs appropriately.
2.8 How many bags must Shelly sell to start showing a profit? (2)
2.9 Calculate the amount of profit on 17 bags. Show all your calculations. (3)
3500
3000
2500
Money in Rand
2000
1500
1000
500
0
0 5 10 15 20 25 30
Number of bags sold
64
Question 3
Mary intends selling cups of coffee at the local taxi rank for extra money. She has organised to set up
her stall at R40 per day and her travelling costs are R14,20 per day. Mary decided to exclude the cost
of water when calculating the cost price per cup of Coffee.
The table below shows how Mary calculated the cost price of ONE cup of Coffee.
QUANTITY BOUGHT COST OF AMOUNT USED FOR COST PER CUP OF
INGREDIENTS ONE CUP COFFEE
3.6 Mary decides to sell the coffee at R10,00 per cup. Her income and expenses graphs are
provided below. Use the graphs to answer the questions that follow:
1200
Mary's Income and Expenses
1000 A
800
Money in Rand
B
600
400
C
200
0
0 20 40 60 80 100 120
No. of cups sold
65
Use the information on the previous page to answer the questions that follow.
3.6.1 Provide the labels for graph A and B and point C (3)
3.6.2 Explain the value given by C in this context. (2)
3.6.3 Approximately how much profit is made when she sells 50 cups of coffee? (4)
3.6.4 Explain whether you believe that Mary should continue with the business if she is able to sell (3)
at least 40 cups a day?
Question 4
Lester rents a hall on the private farm at a fixed cost of R3600 per function. He then hires out the hall
and charges R50 per person (per ticket).
Use the table and the information above to answer the questions that follow:
66
Question 5
Meikhe and his friends plan a tour across South Africa. The tour is set to stretch from Port Elizabeth
down the Garden route to Cape Town. They investigate the rates for GoGo Car hire and eNIGMA Car
Rental. The distance from Port Elizabeth to George is 335km and from George to Cape Town is 434km.
5.1 Provide equations for the cost for both options. (4)
5.2 Show, by calculation, which option would be the best rental for the boys to tour with? (5)
5.3 The table below gives the cost for the two rental options. Provide the values
for A and B.
5.4 Use the table to complete the graphs for both companies on the same set of axes (5)
5.5 Provide the amount of kilometers you could travel when both companies cost the same. (2)
5.6 With the aid of your graph, explain which company you would recommend if the boys decide (3)
to go to George instead?
67
COMPARISON OF TWO RENTAL COMPANIES
8000
7000
6000
5000
MONEY (IN RAND)
4000
3000
2000
1000
0
0 500 1000 1500 2000 2500
NO OF KILOMETERS
GOGO ENIGMA
68
3.2 SOLUTIONS TO PRACTICE QUESTIONS
3.2.1 Tariffs
= R98,16 PCA PA
2.1 Basic Charge is a compulsory monthly amount that one 1A compulsory monthly amount 1
1A whether you use electricity or not.
must pay whether you use electricity or not.
(2)
2.2 PA 2
11 1MA calculating percentage
× 17 PMA
100 1M adding values
PM
= 1,87 + 17 (No mark for R18,87 as it was given)
(2)
= R18,87
2.3 3
First 6kℓ x R7,46 = R44,46 PMA 1MA calculating cost for 6kℓ
Next 9kℓ x R17,39 = R156,51 PMA 1MA calculating cost for 9kℓ
= 15,23 kℓ PCA
(5)
2.4 PMA 2
133kℓ - 53,7kℓ 1MA subtracting correct values
1A amount of water used
= 79,3kℓ PA
(2)
69
Q Solution Explanation T/L
3.1 Total cost (in rands) = 2
1A fixed cost
PA PA 1A variable cost
300 + (the number of persons - 15) x 50 (2)
3.2.1 2
PA 1A substituting total cost (900)
900 = 300 + (n – 15 persons) x 50
PM
(n – 15 persons) x 50 = 600 1M subtracting 300 from 900
n – 15 persons = 12 PM 1M getting 12
n = 27
PCA 1CA number of passengers
(4)
3.2.2 2
PA 1A group 1
Group 1 = 10 learners + 1 teacher
= R250,00 PCA
CALL PACKAGE 2
Total cost = R300 + R0,50 x (0)
= R300 + R0,00
1A total cost
= R300,00 PA 1O conclusion
(6)
PO
Call Package 1 will be cost effective
70
5.1 PA 3
From 7:30 of 06 Jan to 7:30 of 10 Jan it is four full days 1A 4 days / 48 hours
= R444 PCA
1CA amount
(3)
5.2.1 If stopping for a short time you pay much more than the 2O reason 4
amount due. PPO (2)
5.2.2 PSF 3
Open parking: R67 × d + R29 = R500,00 1SF substituting into correct formula
1A number of days
d = 7,03 days PA
1A five days
» 8 days 1A more than 5 days
PA
Shaded parking: 5 days = R500.
PA (4)
So, more than five days you win.
5.2.3 4
The cost escalates quickly. PPA 2O rate of increase.
OR
71
3.2.2 Tax
VAT
Q Solution Explanation T/L
1.1 2
PMA 1MA multiply by 15%
24 1A Answer
ABC: 233 × $79,99 = R12,00 PA
(2)
1.2 PMA 1MA adding values 2
Final Price : $79,99 + $12 = $ 91,99 PA 1A Answer
(2)
2 PMA 2
@28A43 1 MA divide by 1,15
2,24
= $12130,43 PA
1A Answer
(2)
3.1 1MA divide by 1,15 2
>43 1CA Answer
2,24 PMA 1 CA VAT
= R43,48 PCA (3)
R50 – R43,48 = R 6,52
PCA
3.2 20 April 3
PRT PCMA
2 x R150 = R300 x 50% = R150
PRT 1RT correct tarrif
1x R50 = R50 x 50% = R25 PCMA 1CMA correct discounted amount
1RT correct tarrif
1 x R50 = R50 1CMA correct discounted amount
1 x R20 = R20 1M adding all values
PM 1CA simplification
Total: R150+R25+R50+R20 = R245 PCA
23 April
2 x R150 = R300
1 x R50 = R50
1 x R50 = R50
1 x R20 = R20
PM PCA 1M adding all values
Total : R300 +R50+R50 +R20 = R420 1CA simplification
= 0,4167 PCA
(12)
PO
A quarter is 0,25 thus the statement is correct.
72
Income Tax
Q Solution Explanation T/L
1.1 All the money earned before deductions üüO 2O explanation 1
(2)
1.2 Mr KIVIDO üüA 2RT answer 1
(2)
1.3 M = Gross – Deductions 1 RT correct values 2
üM 1 M subtracting values
üRT 1CA answer
= R31 221,25 − R9 362,62
= R21858,63 üCA
üM üRT
N = R9 362,62 – (R4 736,90 + R2251,59 + R245,23 +
R192,70 + 90,25) 1 RT correct values
1 M adding and subtracting values
= R1 845,95 üCA 1CA answer
(6)
1.4 1MA divide by correct values 2
>7 742,4A
ü MA
× 100% 1M multiply by 100
>83 372,74 PM 1CA percentage
= 7,5% PCA
(3)
PM PRT
Thus, 18% of R195 850
1RT R195 850
= 0,18 × R195 850 1M calculating 18%
1A simplification
= R 35 253 PA
(3)
73
Q Solution Explanation T/L
3.1 3
PMA
7,5
Pension = ⨉ 37 537,75 1MA calculating 7,5%
100
= R2 815,33125 ⨉ 12 PMA 1M multiply by12
= R33 783,98 PCA 1CA pension amount
52 5B?,A3
PM 1M divide by 12
= 27
1CA monthly tax
= R6 820,66 PCA
OR
Their total rebate is higher PPO (2)
8? 48?,?4 1MA divide by1,064 2
3.5 Gross monthly salary in 2018/2019 = PMA
2,36B
1CA simplification
= R35 279,84 PCA
OR
100
Gross monthly salary in 2018 = 37537,75 ´ PMA 1MA calculating percentage
106,4
1CA simplification (2)
= R35 279,84 PA
74
Q Solution Explanation T/L
4.1 Tolken PPRT 2RT correct surname (2) 1
4.2 365 days PPRT 2RT Answer (2) 1
4.3 On the last day of the month PPRT 2RT Answer (2) 1
4.4 Expert systems PPRT 2RT Answer (2) 1
4.5 Monthly salary = R168 000 ÷ 12 PM 1MA divide by 12 2
= R14 000 PA 1A Answer (2)
4.6 Percentage contribution A CA from 4.5 2
1 050
= 14 000 x 100% 1M calculating percentage
PM
1CA answer
= 7,5% PCA
(2)
A
4.7 UIF contribution CA from 4.5 2
= 0,01 x R14 000 PM 1M calculating 1 %
= R140 PCA 1CA Answer
(2)
4.8 2
Monthly taxable income = R14 000 – R1050 PM 1M subtracting pension
= R12 950 PCA 1CA answer
Annual Taxable income = R12 950 × 12
=R155 400 PCA 1CA annual taxable income
(3)
4.9 Annual tax payable 3
= 18% of R155 400 PRT 1RT Correct bracket
= R27 972,60 PCA 1CA simplification
= R27 972,60 – R14 958 1CA annual tax payable
= R13 014 PCA 1CA monthly tax payable
= R1 084, 50 PCA
(4)
4.10 Total deductions 1
75
Solution Explanation T/L
5 Joy: 4
Age:52; Salary: R286 500 per annum ; 7% pension;
1 dependent on Medical Aid
= R20 055 PA
1A correct pension amount
PCA 1CA taxable Income
Taxable income = R286 500 – R20 055 = R 266 445
PRT 1RT correct tax bracket
Tax payable: R37062 + 26% × (R266 445 – R205 900)
76
3.2.3 Interest and Hire-purchase
1.3 2
R19 200 + R7 200 1M adding correct values
1CA total amount
=R26 400
PCA (2)
2.1 1
11,5 PMA 1MA calculating percentage
´ R549 000
100 1A interest per year
PA (2)
=R63 135
2.2 Amount received from investment = R26 400 4
1M subtracting amounts
Deposit needed = R63 135
1CA difference
PM
Difference = R63 135 – R26 400
1O explanation
PCA (3)
=R36 735
PO
No, he will not have enough, he will run short of R36 735.
2.3.1 Number of months = 20 ´ 12 3
PA 1A number of months
= 240
77
Q Solution Explanation T/L
3.1 1
R221 180 PPA 2A correct amount
(2)
3.2 1
60
Number of years = PMA 1MA dividing 60 by 12
12 1A number of years
= 5 years PA (2)
3.3 2
11 PA PM 1A correct percentage
Deposit needed = ´ R221 180 1M multiplying by the amount
100 1CA deposit needed
= R24 329,80 PCA (3)
3.4 3
Total payment = Deposit + monthly instalment + residual
PMA
= R24 329,80 + (R2991 x 60) + R99 218 1MA multiplying 2991 by 60
1M adding deposit amount
PM PM 1M adding residual
= R24 329,80 + R179 460 + R99 218 (3)
78
Q Solution Explanation T/L
4 Uncles option 4
1MA calculating percentage
18 PMA 1A amount of interest
Interest = ´ R16 000 ´ 5
100 1CA total amount
= R14 400 PA
Total amount = R16 000 + R14 400
= R30 400 PCA
Personal loan option
1MA calculating percentage
st 16 PMA
1 year interest = ´ R16 000
100
= R2 560
PCA 1CA 2nd year amount
2nd year amount = R16 000 + R2 560 = R18 560
16
2nd year interest = ´ R18 560
100
= R2 969,60
PCA
rd
3 year amount = R18 560 + R2 969,60 = R21 529,60
1CA 3rd year amount
16
3rd year interest = ´ R21 529,60
100
= R3 444,74
th
PCA
4 year amount = R21 529,60+ R3 444,74 = R24 974,34
1CA 4th year amount
16
4th year interest = ´ R24 974,34
100
= R3 995,89
PCA
5th year amount = R24 974,34 + R3 995,89 = R28 970,23
1CA 5th year amount
16
5th year interest = ´ R28 970,23
100
= R4 635,24
Total amount = R28 970,23 + R4 635,24 1CA total amount
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Q Solution Explanation T/L
5.1 Hire purchase agreement is a financial agreement between the 2O explanation 1
shop and the customer about how the customer will pay for the
desired product. PPO (2)
5.2 1
PMA 1MA subtracting correct values
Discount = R7 139,99 – R6 499,00
1CA discount amount
= R640,99 PCA (2)
5.3 2
1A correct percentage
15 PA PMA 1MA multiplying by correct amount
Deposit = ´ R6 499,00
100
= R974,85 (No mark here)
(2)
5.4 1
2A correct percentage
18,5% PPA
5.5 3
PM 1M subtracting amounts
Balance after deposit = R6 499,00 – R974,85
= R5 524,15 PCA 1CA balance after deposit
18,5 PM
Interest charged = ´ R5 524,15 ´ 3 1M calculating the interest
100
= R3 065,90 PCA 1CA interest
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3.2.4 Income and expenses; Profit and loss
OR
Ratio is 3:1
2PA PCA
Thus B × R28 000 = R7 000 Partner
PCA
R28 000 – R 7000 = R21 000
1.3 2
23?,4 PMA PA 1MA calculating a percentage
× R25 000 = R26 875
233 1A answer
1.4 PM 2
A: R 327 700 – (R25 00 + 9 500 + 8 200 + 120 000) 1M adding and subtraction
1CA answer
D
= R 165 000 PCA
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2.3 For 2015: 1RT Correct values 4
PRT 1SF substitution
Percentage profit =
8B7 48B
× 100 PSF 1A percentage for 2015
7743 3B2
= $ 15,22345593% PA 1A Percentage for 2016
1O Comparison
For 2016:
863642
Percentage Profit = 7B3843A × 100
= $ 15,00518617% PA
= R80 PA
3.3 2M Division 4
433 1A Opinion
The large cooldrink = 20ml/R PM
74
The medium
8B3
= 17ml/ R PM
73
PO
Thus large is best
3.4 Tuesdays are slow business days, thus they are trying to draw 2O Opinion 4
customers
PPO
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3.2.5 Cost and selling price; Break-even analysis.
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Q Solution Explanation T/L
2.1 Selling price 2 RT 1
(2)
= R 100,00 per bag üüA
2.2 Cost price 2MA Adding fixed costs 1
üüMA (2)
= R 75,00
Costs Income
2.7 The number of bags she needs to sell to cover her expensesüüEG 2 E Explanation (2) 1
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Q Solution Explanation T/L
2.9 Profit = Income – Expenses üA 1A Profit equation 3
üSF üSF
Profit = (R100,00 × 17) – (R80,00 + (R75,00 × 17)
1SF Income
Profit = R 1 700,00 – R 1 355,00 1SF Costs
1CA Answer
Profit = R 345,00 üCA
(4)
3.1 Cost price of an item is the cost of making that item/ OR/OF 2A Explanation 1
This is the amount that it costs per unit to either manufacture, purchase
the item or to prepare for a service that will be delivered. This amount is
pure cost, no markup or profit added yet üüA (2)
G
3.2 A: 1M division 2
üM
@A?,A4 1A Answer
A: × 4
2333
B: 1M Division
= $3,92 üA
1 A Answer
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Question 4
Q Solution Explanation T/L
4.1 1MA Division by correct values 2
üMA 1CA (2)
D=
7433
= 50 TUQVWTI üCA
43
8000
6000
4000
2000 (5)
0
0 50 100 150 200
No. of people
Rental Hire Out
4.4 üMA 4
1MA subtracting correct values
Difference = R3000 - R3600
1A Answer
= - R 600 üA
1O Conclusion
It is a loss üO
(2)
1
4.5 2O explanation
When the income from the number of tickets sold is equal to the
cost of renting the hall. üüA (2)
4.6 1MA divide by 1,15 3
üMA 1 CA Answer
@8633
= $3130,43 1 MCA subtraction
2,24 üCA
1CA Answer
üMCA (4)
R3600 – 3130,43 = R469,57
üCA
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Question 5
Q Solution Explanation T/L
5.1 3
üSF üMA 1SF correct Fixed cost
Enigma: Cost = R2000 + R1,50 X (distance -350)
1MA variable cost
GoGo: Cost = R3,50 X distance üMA 1MA equation
(3)
5.2 Distance: 769km 3
üSF
Enigma: R2000 + R1,50 X (769km – 350km)
1SF correct values
= R 2628 üA 1A answer
GoGo = R3,50 X 769
= R 2961,50 üCA
1CA answer
B:
2 B33 üMA
= 400km
8,4
üA 1MA Division by 3,5
1A Answer
(3)
5.4 2
GOGO ENIGMA
(6)
5.5 2RT 2
üüRT
approximately 750 km
(2)
5.6 George Distance = 335 km üRT 1RT distance 4
2 O opinion
Thus GoGo is cheaper as the graph is lower
üüO
NOTE: Even though you are given free km, the fixed cost for
Enigma is still R2 000
(3)
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4. EXAMINATION GUIDANCE
PAPER 1
Question 5
Finance, data handling or integrated
question
Probability will be examined in thecontext of one or more of
the other questions.
Each question can contain more than one context.
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Time and mark allocation
Paper 1
Duration Marks
3 hours 150 Marks
If you have 100 hours to prepare for the examination, the following can be used as a guide on how to use your hours:
Paper 1:
QUESTION 1 (30 marks ± 5 marks ONLY taxonomy Level 1.) Short context – mixed questions(Finance and
Data Handling.)
QUESTION 2 – Finance
QUESTION 3 – Data Handling
QUESTION 4 – Finance and Data Handling QUESTION
5 – Finance, Data Handling or integrated
Probability will be integrated in all five questions, where it is appropriate.
GUIDANCE
Set a goal (marks you would like to see on your Matric Certificate) at the beginning of the term,
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5. GENERAL EXAMINATION TIPS
1. Study the matric timetable. Know when you are going to write the papers you have registered for. There
are sometimes two exams on one day so you will have to be super sharp and alert. Be sure to check the
final timetable in case there are any changes.
2. There are less than 123 days to the start of the final exams. This includes all weekends and holidays.
Start today and work every day. Set targets for achievement.
3. Do not miss one day of studying between now and your exams. Work at least two to three hours per
day. Keep healthy and alert.
4. Reading is a hot skill. Reading will change your life. Read at least 1000 words every day. Read everything
you can get your hands on. Read accurately and quickly.
5. Writing is power, but it requires practice. We are all judged, every day, on our writing. We can inspire,
impress, persuade, congratulate and express love in writing. Write at least 400 words every day carefully,
accurately and beautifully.
6. Resources are an essential student companion. Work systematically through your question papers and
Self Study Guide. Don’t wait for your face-to-face classes or broadcasts to explain it all. Look at what you
have to cover for the subject and plan accordingly.
7. Your BMI can help you in matric. Your Body mass Index (BMI) is an indication of how healthy you are.
Calculate your BMI and then exercise and eat healthy throughout the year to keep an optimum BMI.
8. Academic work requires concentration and focus. Every day you should be engaged in intensive,
focused, individual academic work. Turn off iPods, music centres, the TV, the cell phone and have an
intensive and rewarding academic work out every day. Except of course if you are using it to access the
resources. Be diligent and don’t be tempted to watch or access non – academic material. Technology is a
fabulous platform to learn and prepare for the examinations but it can also be a deterrent if you are not
focused and dedicated. Build your brain cells and be the envy of all your friends.
9. Good vibes are good for success. Surround yourself with positive people who want you to succeed. Your
family and friends will be important ibn supporting you in the next 123 days. Be grateful for their support.
10. Matric success requires Planning and hard work. Start planning and working today. Read every day.
Write and calculate every day. Stick to your year plan.
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6. References
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7. Acknowledgements
The Mathematical Literacy Second Chance Self Study Guide Booklet was developed by the following Subject
Specialist:
• Ms Arden Ellie (Eastern Cape Education Department)
• Ms Thembeka Nethe (Free State Education Department)
• Mr Nzimeni Koba (Free State Education Department)
• Mr Peter Kekana (Gauteng Education Department)
• Mrs Zandile Mdiniso (KwaZulu – Natal Education Department)
• Ms Mary Sebela (Limpopo Education Department)
• Mr Kwazinkosi Gwate (Northern Cape Education Department)
The Department of Basic Education (DBE) gratefully acknowledges these officials for giving up their valuable time,
families and knowledge to develop this resource for the children of our country.
A special mention must be made to Ms Masirheni Gladys Nkwinika, the DBE curriculum specialist who, in addition to
her contribution to the development of the booklet, co-ordinated and finalised the process.
The development of the Study Guide was managed and coordinated by Ms Cheryl Weston and Dr Sandy Malapile
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