Mr Robert stay in a semi-detached house and is concerned about the rising electricity costs. After reading about solar power from the newspaper, he is thinking of installing solar panels to reduce his family's electricity bills. The cost of electricity per kilowatt hour (kWh) is known as the electricity tariff rate, which is revised every quarter by SP Power. Information about the electricity tariff rates and monthly electricity consumptions by domestic customers are provided below.

((a))
The electricity tariff rate for Oct - Dec 22 is expected to increase by 8% from Jul - Sep 22 due to geopolitical reasons and shortage of resources.

Calculate the electricity tariff rate for Oct - Dec 22 to 2 decimal places.

Answer (a) ... C/kWh
((b))
Mr Robert is currently with Best Power on a 12 month plan that offers a 6% discount off the electricity tariff rate. Estimate Mr Robert's amount paid for his family's electricity consumption in Oct 2022 after GST.

Answer (b) $...
((c))
Mr Robert decides to consult another electricity provider to enquire about solar energy and solar panel installation. After an assessment is done on his house, he received an information sheet shown in the table below.

Suggest whether Mr Robert should go ahead with installing solar panels for his house.

Justify any decision you make and show your calculations clearly.

Answer (c)

Increase decrease Approximation estimation 中文

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Worked solution

10((a))

1. Calculate the tariff after an 8% increase from 30.17 cents/kWh.

Jul–Sep 22 tariff $=30.17$ cents/kWh.

After an $8\%$ increase,
$30.17\times 1.08=32.5836$

To 2 decimal places,
$32.5836=32.58$

Answer

$32.58$ C/kWh

10((b))

1. Apply the 6% discount to the Oct–Dec 2022 electricity tariff rate.

From part (a), the Oct–Dec 2022 tariff rate is $32.58$ cents/kWh.

After a $6\%$ discount,
$32.58\times 0.94=30.6252$
So the discounted tariff rate is $30.6252$ cents/kWh.

2. Calculate the cost before GST for one month of electricity consumption.

Mr Robert stays in a semi-detached house, so the average monthly consumption is $1195.87$ kWh.

Cost before GST:
$1195.87\times 30.6252=36625.140324\text{ cents}$
$36625.140324\div 100=366.25140324$
So the cost before GST is $366.25140324.

3. Add 7% GST and round the final amount to the nearest cent.

After GST:
$366.25140324\times 1.07=391.888?$
More directly,
$\frac{1195.87\times 30.6252\times 1.07}{100}=391.888?$
Using the calculated value,
$366.25140324\times 1.07=391.888?\approx 391.89$

Answer

$395.47

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Worked solution

10((a))

10((b))

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