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Sagot :
Let's address each part of the question step-by-step based on the given information and calculations:
#### 4.1.1 Write down the tariff in November 2020 for water usage between 6.1 and 10 kl.
The tariff for water usage between 6.1 and 10 kilolitres (kl) in November 2020 is R20.00 per kilolitre.
#### 4.1.2 Determine the number of kilolitres (kl) of water Sam used in September 2020.
To determine the number of kilolitres of water used, we subtract the previous reading from the current reading:
- Previous Reading: 021186 kl
- Current Reading: 021243 kl
Water used = Current Reading - Previous Reading
Water used = 21243 - 21186
Water used = 57 kl
Thus, Sam used 57 kilolitres of water in September 2020.
#### 4.1.3 Sam states that his water bill will be R2 155.00, excluding VAT. Verify, showing ALL calculations, whether his statement is valid.
To verify Sam's statement, we need to calculate the total cost based on the given tariffs and the kilolitres used.
Given tariffs:
- 0-6 kl: R10.00 per kl
- 6.1-10 kl: R20.00 per kl
Water usage breakdown:
- First 6 kl falls under the 0-6 kl tariff.
- Remaining 51 kl (57 kl total - 6 kl) falls under the 6.1-10 kl tariff.
Cost calculations:
1. Cost for the first 6 kl:
[tex]\[ \text{Cost for 0-6 kl} = 6 \, \text{kl} \times R10.00/\text{kl} = R60.00 \][/tex]
2. Cost for the next 51 kl:
[tex]\[ \text{Cost for 6.1-57 kl} = 51 \, \text{kl} \times R20.00/\text{kl} = R1020.00 \][/tex]
3. Total cost (excluding VAT):
[tex]\[ \text{Total cost} = R60.00 + R1020.00 = R1080.00 \][/tex]
Sam stated that his water bill would be R2 155.00, excluding VAT, but the calculated total cost is R1080.00. Therefore, Sam's statement is not valid.
#### 4.1.4 Write down ONE way on how Sam can save water to reduce his water bill.
One effective way for Sam to save water and reduce his water bill is to install water-saving showerheads.
#### 4.2 Ms Theko borrowed R125,000 from ABC bank to buy a car and agreed to pay back the interest of 8.5% that is compounded annually for 2 years.
4.2.1 Calculate the amount of interest that was added at the end of the first year.
To calculate the interest amount for the first year:
- Principal amount: R125,000
- Annual interest rate: 8.5%
Interest calculation for the first year:
[tex]\[ \text{Interest} = \text{Principal amount} \times \text{Interest rate} \][/tex]
[tex]\[ \text{Interest} = R125,000 \times 0.085 \][/tex]
[tex]\[ \text{Interest} = R10,625.00 \][/tex]
Thus, the amount of interest added at the end of the first year is R10,625.00.
#### 4.1.1 Write down the tariff in November 2020 for water usage between 6.1 and 10 kl.
The tariff for water usage between 6.1 and 10 kilolitres (kl) in November 2020 is R20.00 per kilolitre.
#### 4.1.2 Determine the number of kilolitres (kl) of water Sam used in September 2020.
To determine the number of kilolitres of water used, we subtract the previous reading from the current reading:
- Previous Reading: 021186 kl
- Current Reading: 021243 kl
Water used = Current Reading - Previous Reading
Water used = 21243 - 21186
Water used = 57 kl
Thus, Sam used 57 kilolitres of water in September 2020.
#### 4.1.3 Sam states that his water bill will be R2 155.00, excluding VAT. Verify, showing ALL calculations, whether his statement is valid.
To verify Sam's statement, we need to calculate the total cost based on the given tariffs and the kilolitres used.
Given tariffs:
- 0-6 kl: R10.00 per kl
- 6.1-10 kl: R20.00 per kl
Water usage breakdown:
- First 6 kl falls under the 0-6 kl tariff.
- Remaining 51 kl (57 kl total - 6 kl) falls under the 6.1-10 kl tariff.
Cost calculations:
1. Cost for the first 6 kl:
[tex]\[ \text{Cost for 0-6 kl} = 6 \, \text{kl} \times R10.00/\text{kl} = R60.00 \][/tex]
2. Cost for the next 51 kl:
[tex]\[ \text{Cost for 6.1-57 kl} = 51 \, \text{kl} \times R20.00/\text{kl} = R1020.00 \][/tex]
3. Total cost (excluding VAT):
[tex]\[ \text{Total cost} = R60.00 + R1020.00 = R1080.00 \][/tex]
Sam stated that his water bill would be R2 155.00, excluding VAT, but the calculated total cost is R1080.00. Therefore, Sam's statement is not valid.
#### 4.1.4 Write down ONE way on how Sam can save water to reduce his water bill.
One effective way for Sam to save water and reduce his water bill is to install water-saving showerheads.
#### 4.2 Ms Theko borrowed R125,000 from ABC bank to buy a car and agreed to pay back the interest of 8.5% that is compounded annually for 2 years.
4.2.1 Calculate the amount of interest that was added at the end of the first year.
To calculate the interest amount for the first year:
- Principal amount: R125,000
- Annual interest rate: 8.5%
Interest calculation for the first year:
[tex]\[ \text{Interest} = \text{Principal amount} \times \text{Interest rate} \][/tex]
[tex]\[ \text{Interest} = R125,000 \times 0.085 \][/tex]
[tex]\[ \text{Interest} = R10,625.00 \][/tex]
Thus, the amount of interest added at the end of the first year is R10,625.00.
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