If you have a standard tank hot water heater then your hot water is being kept hot by the water heater around the clock. It doesn't matter if you're on vacation, at work or asleep the water heater is still going to keep the water hot. So it would make sense to tell the water heater to not heat the water when you are away and are not going to be using hot water.
According to the Dept. of Energy you can save 5-12% on your costs by installing a timer on your hot water heater that will turn it off when you're asleep or to avoid high cost peak energy times. However they do point out that timers are not as effective on gas water heaters.
At Home Depot you can buy an Intermatic brand 40amp water heater timer for $40 (pictured).
With a typical hot water heater costing about $400 to run per year a 5-12% reduction would cut your costs $20 to $48 per year. So it will take 1-2 years to pay back the cost of the hot water timer.
Buying and installing a water heater timer is a good buy.
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