Coaching Centre
Household bills
Reading electricity, gas and water bills: meter readings, usage charges, daily supply charges, solar feed-in credits, GST, and the running cost of appliances in kWh.
Every household pays for electricity, water and usually gas. The bills look complicated, but each one is the same two parts: what you used, times a rate, plus a fixed charge for being connected. Once you can read one, you can read them all, and you can check whether switching to a cheaper plan is worth it.
Electricity bills
Electricity is measured in kilowatt-hours (kWh). One kWh is the energy used by a $1$ kW appliance running for $1$ hour. A bill has:
- a usage charge: kWh used $\times$ price per kWh;
- a daily supply charge: a fixed amount for every day of the billing period, even if you use nothing.
Usage is the difference between the current and previous meter readings. Prices on residential bills include GST.
A household's meter read $48\,213$ kWh at the last bill and $49\,152$ kWh now, $91$ days later. The plan charges $34.10$ cents per kWh and a supply charge of $115.2$ cents a day. Find the bill.
Check Example 1. Then work out what share of the bill is the supply charge. Would halving your usage halve your bill?
Add $400$ kWh of solar exports. How much does that save? Compare with using those $400$ kWh yourself instead of buying them at $34.10$ cents.
Solar feed-in credits
Homes with rooftop solar sell the power they don't use back to the grid and get a feed-in credit, often only a few cents per kWh. Because buying power costs about ten times as much as selling it, solar saves the most when you use it as it's made: running the dishwasher or charging the car in the middle of the day.
Gas and water
Gas works the same way, but usage is measured in megajoules (MJ). Water is measured in kilolitres (kL), where $1$ kL $= 1000$ L. In Sydney, water bills also include fixed service charges for water and wastewater.
With example prices: (a) a gas bill for $4350$ MJ at $3.9$ cents per MJ plus $70$ cents a day for $91$ days; (b) water usage of $62$ kL at $\$2.67$ per kL. Find each charge.
Running an appliance
Energy used (kWh) $=$ power (kW) $\times$ time (hours). A $2400$ W heater is $2.4$ kW. Run for $5$ hours a day for $30$ days, it uses $2.4 \times 5 \times 30 = 360$ kWh. At $32$ cents per kWh, that's $\$115.20$ a month, which is why heating shows up on winter bills.
Your turn
A bill covers $90$ days. The household used $1240$ kWh at $30.8$ cents per kWh, and the supply charge is $110$ cents a day. Find the total.
Show the working
Usage: $1240 \times 0.308 = \$381.92$. Supply: $90 \times 1.10 = \$99$. Total: $\$480.92$.
An electricity meter read $12\,480$ kWh last quarter and reads $13\,215$ kWh now. Find the usage.
$13\,215 - 12\,480 = 735$ kWh.
Find the usage charge for $735$ kWh at $32$ cents per kWh.
$735 \times 0.32 = \$235.20$.
Find the supply charge for $92$ days at $98$ cents a day.
$92 \times 0.98 = \$90.16$.
A home exports $420$ kWh of solar power at a feed-in rate of $6$ cents per kWh. Find the credit.
$420 \times 0.06 = \$25.20$.
An electricity bill is $\$286$, including GST. How much GST does it include?
$286 \div 11 = \$26$.
Find the cost of $48$ kL of water at $\$2.67$ per kL.
$48 \times 2.67 = \$128.16$.
Which statement about the daily supply charge is true?
The supply charge is a fixed daily cost of being connected to the network.
A $\$425.03$ bill covers $91$ days. Find the average cost per day, to the nearest cent.
$425.03 \div 91 \approx \$4.67$.
Exam style: A $2400$ W heater runs $5$ hours a day for $30$ days. Electricity costs $32$ cents per kWh. Find the cost.
$2400$ W $= 2.4$ kW. Energy: $2.4 \times 5 \times 30 = 360$ kWh. Cost: $360 \times 0.32 = \$115.20$.
Exam style: A $92$-day bill has usage of $860$ kWh at $33$ cents per kWh, a supply charge of $105$ cents a day, and a solar credit of $310$ kWh at $5$ cents per kWh. Find the amount due.
Usage: $860 \times 0.33 = \$283.80$. Supply: $92 \times 1.05 = \$96.60$. Credit: $310 \times 0.05 = \$15.50$. Total: $283.80 + 96.60 - 15.50 = \$364.90$.