My gas bill is $25-30. Gas water heater, dryer and kitchen stove.
Raising the water only 60* would be pretty cold water. I have mine set to 120*. Incoming is 36-38*
Yeah, 60 degree rise is probably about the overall temp rise for a shower, meaning 30 gallons of water per day total usage, not just hot water. My point is $25 for electric hot water per month is unreasonably low for a family of 5.
In your case, how much do you pay per MCF or gallon? Gas is usually cheaper per BTU than electricity, especially natural gas. Although there is more wasted energy with a gas water heater.
Electric elements are 100% efficient at transforming electricity to heat. So $25 per month divided by $.18 per KwH equates to 139 KwH per month to heat water (25/.18). Converted to BTU, that is 473,889 (3,412 BTU in 1 KwH). One BTU raises one pound of water 1 degree Fahrenheit. So 473,889 BTU would raise 5924 pounds of water 80 degrees F (473,889/80). A gallon of water weighs 8.3 lbs. So 5924 pounds of water is 714 gallons (5924/8.3). Over 30 days, that is just under 24 gallons per day (714/30), which is not very much hot water. In reality, some additional energy (5-10%) is lost to standby losses, so even less hot water per day is available.
By comparison, natural gas at 7$ per MCF (about 1,000,000 BTU) would cost $3.32 for 473,889 BTU of energy. Even if the gas water heater was 65% efficient, it would only increase the cost to $5.10. So natural gas is about 1/5 the cost of electric for hot water at the above energy prices (even for an inefficient gas water heater), all else being equal.