That seems kind of high, but then I don't know what your electric rates are. How many KWhours do you use in a month?
If you are using lots more KWhours than you think you should be, I would wonder if your electric meter is working accurately, and if so, where the excess electricity is going or being used. Having someone watch the electric meter as you individually turn on breakers can help you determine if any circuit has "phantom" loads. If the wheel on the meter turns when all the breakers except one are off, that circuit is using electricity.
Do you have a well? Pumps and other parts of water systems can go bad and use a lot of electricity. If your pump cycles too often, you might be losing water somewhere in your system. I once had the internal check valve in my submersible pump fail, which allowed the water in the pressure tank to quickly leak back into the well. The pump would cycle on and off about every 5 minutes. I will never install another submersible pump without adding an external check valve, which fixed the problem fairly cheaply. We pump a lot of water in the Summer, and our highest electric use is always in August, although part of that is because the air conditioning is also used a lot then.
We heat with natural gas, both the home and our hot water and I think that is about the cheapest way to go here. But you have to have access to a gas line. Propane is lots more expensive than natural gas, but if electric rates are high enough, it might pay to heat your water that way. If natural gas is an option, it might well be the best investment for heating air or water.
Years ago we lived in a mobile home that was all electric. It wasn't super well insulated and it gets very cold here in the Winter. Sometimes I had electric bills that went over $300, and that was a lot more money back in 1976 than it is now! I installed a special mobile home wood stove, doing the installation legally with permits and inspections. The wood stove allowed my electric bills to go down to about $100/month and I figured the stove payed for itself in a couple of years. But then a few years later, my insurance company decided that they would cancel ALL of the policies they had on mobile homes with wood stoves. I ended up paying huge insurance rates because my mobile home had a wood stove. We ended up building a new, much larger, well insulated conventional house and the mobile home went down the road. We were able to hook up to the natural gas line when we built the house, and I did not add any wood burning capability to the new construction. Our total energy bills for the home very seldom go over $300/month now, and probably average about $200. Gas use goes up when it is cold outside, but in the Summer, the gas bill is sometimes less than $30/month, and we use quite a bit of hot water all the time.
If I was pretty sure that an electric water heater was using excess power, I would test that theory by shutting off the water heater at the breaker for a set time period of maybe a week, and then compare the electric use for the same amount of time with the water heater on. I know that would be a hassle, but if you heated the water you needed for household use on the electric range, it might show you how much the water heater is actually using.
After my parents moved off the farm, we sold the buildings and 10 acres to a couple. A few months later, they complained that the electric use was out of sight, and it was lots higher than we had ever experienced. It turned out that somehow the water heater, which had been in the house at least 30 years, had gone bad. They replace it, and the electric bill came back down. I don't know what was wrong with the heater, but obviously, they can go bad on you.
To answer your question about water temperature, everything I have ever read has said that keeping the water at a lower temperature (usually 120 degrees) is supposed to be the most efficient for home use. Good luck, hope you find out what is causing the high bills!
