Question

A large appliance such as a water heater is only running when it has clicked on and is actually heating water. The time your water heater is on varies according to how
much you use hot water-do laundry, take showers, run the dishwasher. The national average is 3 hours per day.
a. If a water heater uses 4,200 watts, find the daily cost of running it at a cost of $0.11 per kilowatt-hour. Round to the nearest ten cents.
b. Find the annual cost of running the water heater to the nearest $10.
c. A certain energy-saving water heater sells for $1,100. It will save 36% in energy costs per year compared to the water heater from parts a and b. What will be the
approximate annual cost of running this water heater? Round to the nearest ten dollars.
d. In how many years will the new water heater "pay for itself"?

Answer 1

a) Total cost (per day) ≈ $1.40

​b) Total cost (per year) ≈ $510

c) New annual cost = $327

d) The number of years that the water heater pays for itself is; approximately 4 years

How to calculate Energy Bill?

Wattage per hour = 4200 Watts per hour

Number of hours per day = 3 hours

Cost per unit = $0.11 per kilowatt-hour

Savings rate = 36%

Cost water heater = $1,100

a) The total wattage is the product of the wattage per hour and the number of hours;

Total wattage (per day) = Wattage per hour × Number of hours

= 4,200 watts per hour × 3 hours

= 12,600 watt-hours

= 12.6 kilowatt-hours

​

The total cost is then the product of the total wattage and the cost per unit:

Total cost (per day) = Total wattage × Cost per unit

Total cost (per day) = 12.6 kilowatt-hours × $0.11 per kilowatt-hour

Total cost (per day) = $1.386

Total cost (per day) ≈ $1.40

​

b) The total cost in a year is the product of the total cost in a day and the number of days in a year. There are 365 days in a year (assuming no leap year).

Total cost (per year) = Total cost (per day) × Number of days in a year

Total cost (per year) = $1.40 × 365

Total cost (per year) = $511

Total cost (per year) ≈ $510

​

c) We are told that this new water heater saves 36% of annual cost. Thus;

Amount saved = 36% * 510 = $183.6

Thus;

New annual cost = $510 - $183 = $327

d) The number of years that the water heater pays for itself is;

1100/327 = 3.36 or approximately 4 years

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