Directorate: Curriculum FET
SUBJECT and
GRADE
TERM 1
TOPIC
AIMS OF LESSON
RESOURCES
INTRODUCTION
CONCEPTS AND
SKILLS
ACTIVITIES/
ASSESSMENT
CONSOLIDATION
VALUES
MATHEMATICAL LITERACY
Week 3
FINANCE: TARIFFS
The following type of tariffs will be focused on:
Water, Electricity, Cellphone Data, Banking Fees and Transport Tariffs (Taxi)
Paper based resources
Digital resources
Refer to your Textbook:
https://www.education.gov.za/Informationfor/Learners/Video
Consult: Finance – Tariffs for more information
Tutorials.aspx
• Tariffs have already been covered in Grade 10 and 11. In Grade 12, this section is consolidated.
• The main focus of explanation in this lesson plan will be the usage of sliding scales that can be find in water
and electricity tariffs
The following skills and concepts are covered in this lesson plan:
• Water tariffs: The tariff table should be used to determine the water cost according to a sliding scale.
• Electricity tariffs – The different tariff structures will be used to determine the cost according to a sliding
scale, a flat rate, a fixed cost plus a flat rate. The understanding of a stepped graph as well as setting up or
generating a formula will also be covered.
• Cellphone Tariffs (Data) – Using the table, formula and graphs to determine cost as well as drawing of a
graph from a table of values or formula/ tariff descriptions and other related skills such as conversions
• Banking Fees/Tariffs – Using the tariff/fee structure in a table to determine bank fees/charges and other
related skills such as conversions
• Transport Tariffs (Taxi) – Using the tariffs in words to determine cost, setting up a formula and doing reverse
calculations to determine the distance if the cost is given.
• The material consists of a lesson plan, with activities with notes and examples to work through.
• Study or work through the examples to guide you to do the activities 1 - 5
• Break up the activities to be done over the week.
• Supplement activities with activities in your textbook.
• It is important to study previous papers to see questions that relates to the topic done now. By doing this, you
will see how questions could be posed in the end-of-year-examination.
• Thank you for showing your first step of independent learning.
• Use services responsible in order to save on costs
WATER TARIFFS:
Some important Notes:
First calculate the kℓ per interval:
Etc. Subtract the endpoints of the
interval to get the maximum amount
of kℓ used per bracket:
Interval 1: 6kℓ used
Interval 2: 10 – 6 = 4
Interval 3: 35 – 10 = 25
Interval 4: The amount use in this
interval is the amount above 35 –
35 etc. 38 – 35 = 3
Adding the kilolitres used =
6+4+25+3 = 38 kℓ
Use the given table to
do your initial
calculations
•
The cost of water is
determined according
to a sliding scale.
Water cost according to
this tariff structure DO
NOT mean that if you
use 38 kl of water then
you
calculate
it
according to a flat rate,
namely:
38kℓ × 69,10 = R2 625,80.
This
is
TOTALLY
WRONG. X
•
Water tariff charges
0 – 6 kℓ
More than 6 – 10kℓ
More than 10 – 35 kℓ
More than 35 kℓ
Total:
Water
usage
is
measured in kilolitre
(kℓ)
•
Calculate the VAT (15%) inclusive water
Cost, if 38 kℓ of
water was used.
Tariff summary
(in kilolitre)
•
Tariff
Rand per kilolitre
(VAT Exclusive)
6
×
15,50 = 93,00
4
×
22,25 = 89,00
25
×
31,45 = 786,25
3
×
69,10 = 207,30
38 kℓ
R 1 175.55
VAT inclusive = R 1 175.55 × 1,15
= R1 351,88
VAT (Value Added
Tax) is charge on water
cost
THE CORRECT
CALCULATION USING THE
SLIDING SCALE: ✓
Each interval has its own tariff:
Interval 1: 6 × 15,50 = 93.00
Interval 2: 4 × 22,25 = 89.00
Interval 3: 25 × 31.45 = 786.25
Interval 4: 3 × 69,10 = 207.30
Total:
R 1 175.55
ACTIVITY 1:
The TABLE below shows the stepped water tariff rates (sliding scale) for residential properties in Cape Town.
As from 1 February 2018 level 6 tariffs were charged.
TABLE: Stepped water tariff rates (sliding scale) for residential households in Cape Town (Adapted)
STEP VOLUME/AMOUNT OF
LEVEL 4
LEVEL 6
WATER USED
R/kℓ
R/kℓ
(1 kℓ = 1 000 LITRES)
(INCLUDING VAT –
(INCLUDING VAT–
15%)
15%)
1
more than 0 kℓ to 6 kℓ
R4,65
R29,93
2
above 6 kℓ to 10 kℓ
R17,75
R52,44
3
above 10 kℓ up to 20 kℓ
R25,97
R114,00
4
above 20 kℓ up to 35 kℓ
R43,69
R134,00
5
above 35 kℓ up to 50 kℓ
R113,99
R912,00
6
more than 50 kℓ
R302,24
R912,00
[Source: capetown.gov.za]
Use the Table above to answer the questions that follow:
1. What is the tariff on LEVEL 4 if a household used an amount of water that is above 20 kℓ up
to 35 kℓ (Step 4)?
2. In which STEP/INTERVAL will you pay R52,44 on Level 6?
3. Calculate the VAT exclusive tariff of STEP 1 of Level 6.
4. Use the table to calculate the amount a household will have to pay on Level 4 for consuming 15 kℓ.
5. Use the table to calculate the amount a household will have to pay on Level 6 for consuming 23 kℓ.
6. Calculate how much more a household will pay on Level 6 compared to Level 4 for consuming 37kℓ.
Remember:
1. Use the given table.
2. Calculate the water
per step/interval
3. Check if the
volume/amount of
water adds up to the
volume/amount of
water used.
4. Multiply with the
tariff per
step/interval
5. Add the amounts in
Rand per interval to
get the total cost.
ELECTRICITY TARIFFS:
1. Electricity is charged per kWh (KiloWatt – hour) in cents or rand.
2. Electricity can also be charged according to a sliding scale or it can be charged at a flat rate.
3. If charged according to a sliding scale, use the same procedure as explained in water tariffs.
4. There’s currently two payment systems for electricity, namely pre-paid and on a contract basis.
ACTIVITY 2:
Electricity purchase blocks for 20 Amp
Traiffs
Block 1
Block 2
0 – 350 kWh
More than 350 kWh (>350)
Tariff (cent / kWh)
2017
104.26
118.00
2018
106.56
120.60
1. Calculate in Rand the electricity costs for the following monthly consumption:
1.1 140 kWh in 2018
1.2 380 kWh in 2017
1.3 Calculate the percentage increase in electricity charges for Block 2 tariffs from 2017 to 2018.
2. A local municipality charges 124,5c / kWh (VAT inclusive) for pre-paid electricity.
Calculate how many units in kWh a household will get if R500 of pre-paid electricity
is purchased.
3. Use the following TABLE to answer the question that follow:
Block 1
Block 2
Block 3
Block 4
Residential consumption
All tariffs are 15% VAT exclusive
0–50kWh
R0,9015 per kWh
51–350kWh
R1,0161 per kWh
351–600kWh
R1,3594 per kWh
Above 600 kWh
R1,6314 per kWh
Calculate the VAT inclusive amount to be paid for the consumption of 400 kWh
Question 2:
This is an
example of a
flat rate.
NOTE THE
FOLLOWING:
1. In this case electricity is
charged according to a
sliding scale.
2. Use the same procedure
as explain in water
tariffs.
3. Use the table to write
down the units and
calculations per block.
4. Convert tariffs or total
cost in cents to rand by
dividing
by
100
(Reason: There’s 100
cents in 1 Rand)
Etc.
Convert 106,56c to rand
= 106,56 ÷ 100 =
R1,0656
Question 1.3:
Use the
percentage
increase
formula.
Examiners
expect you to
know by now
the formula.
4. The stepped graph below shows the tariff for a certain block. Use the graph to answer the
questions that follow:
TYPE OF GRAPH:
Stepped Graph
This indicates that the value
is included or in this case it is
the starting value.
This indicates that the value
is not included or less than the
value.
Graph shows the tariff per
block/interval.
The horizontal axis shows the
units in kWh.
The vertical axis shows the
tariff per block/interval.
Complete the following:
4.1 0 to less than (<) ….. kWh tariff is R200
4.2 200 to less than (<)400 kWh tariff is ….
4.3 …… to less than 600 kWh tariff is R600
5. The charge for electricity in one of the cities consists of a fixed rate of R55 per month, plus a rate of
R0,80 per kWh.
5.1 Calculate the monthly cost if a household used 243 kWh for a month.
5.2 Write down a formula for determining the monthly cost in the form:
Monthly cost (in rand) = …
This indicate the tariff for
block / interval of kWh used.
How to set up a
formula for this type
of scenario:
Parts of formula:
Fixed cost + tariff ×
units as in this case.
ACTIVITY 3
CELL PHONE DATA TARIFFS:
John needs data to do research. She finds one of the providers is offering internet usage according to the
following rates:
OPTION 1
500 MB (megabytes)
Fixed monthly cost
Additional monthly
cost
R150
50c for every MB used over 500
MB
OPTION 2
1 GB (gigabyte, 1 000 MB = 1
GB)
R200
50c for every MB used over 1 GB
John needs to choose between OPTION 1 and OPTION 2
1. OPTION 1 can be represented by the following formula:
Cost (in Rand) = 150 + 0.5 × (number of megabytes used – 500)
Calculate the cost of using 900 MB on OPTION 1.
How to express this in a
sum or formula:
Etc. 1 200 MB – 1 000
MB
For the formula see the
OPTION 1’s formula in
Question 1 as an example.
2. The following table shows the monthly cost for OPTION 2.
Monthly Cost for OPTION 2:
Number of MB
0
600
used each month
Cost (In Rand)
200
200
Conversion of GB to
MB:
1 000 MB = 1 GB
800
1 000
1100
1500
1800
200
200
250
450
A
2.1 Calculate the value of A.
2.2 Write down a formula that can be used in OPTION 2 in the form:
Cost (In Rand) = …
2.3 The graph of OPTION 1 is drawn. On the same set of axes draw the graph of OPTION 2.
For the drawing of the
graph see OPTION 1’s
graph as an example.
NB: Normally in the Gr 12
National Examination
Papers grids will be
provided. You should be
able to interpret the
following:
1. What is display on the
horizontal axis?
2. What is display on the
vertical axis?
3. What is the intervals on
the different axis for
example: Use the
following procedure:
Count the intervals
/lines, excluding 0’s
line, to the first value
displayed in this case
500. So the number of
lines up to 500 is 5.
Divide 500 by 5 (500 ÷
5 = 100) So each
interval or line
2.4 Use the graphs drawn in 2.3 to determine which of the two options would you advise John to take if he represents 100. So from
the left to right is: 0,
only want to spend R350 on data. Justify your answer.
100, 200, 300, 400,
500.
Technique: When working in a graph/table it is
4.
The same procedure
essential to use your ruler:
can be followed to
1. Identify the value and
determine the
2. place your ruler in this case horizontally in
intervals/line’s value
line with the value, and
on the vertical axis
3. do your interpretation as required from the
question.
ACTIVITY 4
BANK FEES:
The following TABLE shows the bank fees/charges for certain transactions of Bank A and Bank B.
Use the table to answer the questions that follow:
Transaction
Withdrawal at Banks Own ATM
Withdrawal at another bank’s ATM
Cash deposit at branch
BANK A fees
R7 per R1 000 or part
thereof
R10 + R2 per R100 or part
thereof
R30 + R2 per R100 or part
thereof
BANK B fees
R8 per R1 000 or part thereof
R12 per R1 000 or part thereof
R80 + R2.50 per R100 or part
thereof
Cash deposit at own ATM
R1 per R100
R1.10 per R100
Cash withdrawal at till point
R2
R1.20
1. Identify the place where you will pay the cheapest for withdrawals.
2. Calculate the fee to be paid if R3 800 is withdrawn from Bank’s B own ATM.
3. Calculate the fee to be paid if R4 000 is withdrawn from another ATM and the bank account is
at Bank A.
4. If R9 500 needs to be deposited, calculate the difference in fees between Bank A and Bank B if
it needs to be done at a branch.
ACTIVITY 5
TRANSPORT TARIFFS:
• The most commmon means of transport in South Africa are train, taxi/uber and bus.
• Other means of transport which is more business related is air travel (aeroplanes).
• Single fares (one way only) and Return trip fares (there-and-back)
• Fares are generally based on distance travelled, the cost of fuel, wear and tear and the type of transport.
NB: Banking fees also
contain percentage:
For example: Withdrawal
fees: R4.50 + 1.5% of
amount
UNDERSTANDING:
Per R1 000 or part thereof
OR
per R100 or part thereof:
The amount should be
divided by 1 000 OR 100
to get the number of
1 000’s or 100’s for the
specific amount.
For example: If an
amount of R4 300 is
involved. Then to get the
number of 1000’s:
4 300 ÷ 1 000 = 4,3
(1 000’s)
4,3 should be rounded
up to 5 due to the
statement ‘or part
thereof’. So,
5 (1 000’s) in this case
needs to be used in the
calculations determining
the banking fees.
TRANSPORT TARIFFS:
TAXI – FARES:
Jackie is the driver of a metered taxi. The company he works for charges the following for a single trip:
• A minimum call-out fee of R50 trip and for the first three kilometres free.
• Thereafter, R12,00 for each additional kilometre or part thereof
John’s taxi company charges a flate rat of R14,50 per km
1. The distance for a single trip is 80 km. Francois makes the statement that John’s taxi company
will be the cheapest. Verify, showing all your calculations if his statement is valid .
2. Write down a formula that Jackie can use to calculate the total cost in rand per single trip in the form:
Total cost (in rand) per single trip = …
3. A client pays Jackie R1 214 for a single trip. Determined the distance travelled during this trip.
4. Mrs Majola hires a taxi from Jackie’s company to take her to a meeting venue 8 km from
her home.
The meeting is scheduled to take exactly ONE hour and she requests that the taxi wait for
her back home.
The company charges an extra R100 per hour if the taxi has to wait for a client and the trip
will be charged as a single trip.
Calculate the total taxi fare Mrs Majola will pay for this trip.
Verification
Questions: Your
conclusion should be
back up by
calculations. Make use
of headings to put up
your ‘argument’.
For Example:
• Cost of Jackie’s
company +
calculations
• Cost of John’s
company +
calculations
• Conclusion
Question 2
Setting up a formula:
Consider the following:
• Fixed cost
• Free km
• Rate per km after
the free km
• Check how you are
calculating the cost
and set up your
formula in a similar
way.
ANSWERS
ACTIVITY 1:
6.
1. R43,69
STEP VOLUME/AMOUNT OF
WATER USED
(1 kℓ = 1 000 LITRES)
2. Step 2 or above 6 kℓ to 10,5 kℓ
1
2
3
4
5
6
3. VAT Exclusive tariff of STEP 1 LEVEL 6 = R29,93 ÷ 1,15
≈ R26,03
4.
STEP VOLUME/AMOUNT OF
WATER USED
(1 kℓ = 1 000 LITRES)
1
2
3
4
5
6
more than 0 kℓ to 6 kℓ
6
above 6 kℓ to 10 kℓ
4
above 10 kℓ up to 20 kℓ 5
above 20 kℓ up to 35 kℓ
above 35 kℓ up to 50 kℓ
more than 50 kℓ
Total:
15
LEVEL 4
R/kℓ
(INCLUDING VAT –
15%)
× R4,65 = 27,90
× R17,75 = 71,00
× R25,97 = 129,85
R228,75
5.
STEP VOLUME/AMOUNT OF
WATER USED
(1 kℓ = 1 000 LITRES)
1
2
3
4
5
6
LEVEL 6
R/kℓ
(INCLUDING VAT–
15%))
6 × R29,93 = 179,58
4 × R52,44 = 209,76
10 × R114,00 = 1 140,00
3 × R134,00 = 402,00
more than 0 kℓ to 6 kℓ
above 6 kℓ to 10 kℓ
above 10 kℓ up to 20 kℓ
above 20 kℓ up to 35 kℓ
above 35 kℓ up to 50 kℓ
more than 50 kℓ
Total:
23
R1 931,34
more than 0 kℓ to 6 kℓ
6
above 6 kℓ to 10 kℓ
4
above 10 kℓ up to 20 kℓ 10
above 20 kℓ up to 35 kℓ 15
above 35 kℓ up to 50 kℓ 2
more than 50 kℓ
Total:
37
STEP VOLUME/AMOUNT OF
WATER USED
(1 kℓ = 1 000 LITRES)
1
2
3
4
5
6
more than 0 kℓ to 6 kℓ
6
above 6 kℓ to 10 kℓ
4
above 10 kℓ up to 20 kℓ 10
above 20 kℓ up to 35 kℓ 15
above 35 kℓ up to 50 kℓ 2
more than 50 kℓ
Total:
37
LEVEL 4
R/kℓ
(INCLUDING VAT –
15%)
× R4,65 = 27,90
× R17,75 = 71,00
× R25,97 = 259,70
× R43,69 = 655,35
× R113,99 = 227,98
R1 241,93
LEVEL 6
R/kℓ
(INCLUDING VAT–
15%))
× R29,93 = 179,58
× R52,44 = 209,76
× R114,00 = 1 140,00
× R134,00 = 2 010,00
× R912,00 = 1 824,00
R5 363,34
Difference between Level 4 and 6 = R5 363,34 - R1 241,93
= R4 121,41
ACTIVITY 2
1.1
Electricity purchase blocks for 20
Amp Traiffs
Block 1
0 – 350 kWh
Block 2
More than 350 kWh
(>350)
140
3.
Tariff (cent / kWh)
2018
× 106.56 = 14 918,4 c
= R149,18
1.2
Electricity purchase blocks for 20 Amp
Traiffs
Block 0 – 350 kWh
350
1
Block More than 350 kWh (>350) 30
2
Total:
380
1.3
Percentage increase =
=
𝑵𝒆𝒘−𝑶𝒍𝒅
𝟏𝟏𝟖,𝟎𝟎
2. Pre-paid charges in rand = R1,245
Number of units = R500 ÷ R1,245
≈ 401,606 units
2017
× 104.26 = 36491c
= R364,91
× 118.00 = 3 540
= R 35,40
R400,31
× 100%
𝑶𝒍𝒅
𝟏𝟐𝟎,𝟔𝟎−𝟏𝟏𝟖,𝟎𝟎
≈ 2,2%
Tariff (cent / kWh)
x 100%
Residential consumption
All tariffs are 15% VAT exclusive
Block 1
0–50kWh
50 ×
R0,9015 = 45,075
Block 2
51–350kWh
300 ×
R1,0161 = 304,83
Block 3
351–600kWh
50 ×
R1,3594 = 67,97
Block 4
Above 600 kWh
Total
400
R417,88
⸫ R417,88 × 1,15 = R480,56
4.1 200
4.2 R400
4.3 400
5. Monthly cost = R 55 + 0.80 × 243
= R249,40
6. Monthly cost = R 55 + 0.80 × Units used
ACTIVITY 3
1. Cost (in Rand) = 150 + 0.5 × (number of megabytes used – 500)
= 150 + 0.5 × (900 – 500)
= 350
2.1
A = 200 + 0.5 × (1 800 – 1 000)
= 200 + 0.5 × (800)
= R600
2.2
Cost (In Rand) = 200 + 0.5 × (number of megabytes used – 1 000)
2.3
2.4 Option 2. More data will be given than Option 1.
ACTIVITY 4
1. At till points
2. Fee = 3 800 ÷ 1 000
= 3,8 ≈ 4
=4×8
= R32
3. Fee = 10 + 2 × (4 000 ÷ 100)
= 10 + 2 × 40
( 40 is the number of R100’s)
= R90
4. Bank A = 30 + 2 × (9 500 ÷ 100)
= 30 + 2 × 95
= R220
Bank B = 80 + 2,50 × (9 500 ÷ 100)
= 80 + 2,50 × 95
= R317,50
Difference = 317,50 – 220 = R97,50
ACTIVITY 5
1. Jackie’s company’s total cost = 50 + 12 × (80 – 3)
= 50 + 12 × 77
= R974
John’s company’s total cost = 80 km × R14,50 = R1 160
Conclusion: Francois is WRONG.
2. Total cost (in rand) per single trip = 50 + 12 × (distance in km – 3)
3. Distance travelled:
50 + 12 × (distance in km – 3) = 1 214
= 1 214 – 50
= 1 164 ÷ 12
= 97
Distance in km = 97 + 3
= 100
4. Total cost = 50 + 12 × (8 – 3)
= 110
= 110 + 100
= R210