Without going to an outside service, you can buy the chemicals for about $30 a month, unless you have some incontinent swimmers. Chemicals to lower pH and prevent algae would run another $10.
Electricity, compared to your A/C bill, would be negligible (less than $5). Only a pool heater in winter would actually have an impact on your bill.
The big drawback to do-it-yourself pool maintenance is the time. First you need a couple of hours every week, preferably a little time each day too, to check on the skimmers. Weekly checks on chlorine and pH are required, and some adjustment is usually required. Topping off water level and backwashing doesn't take that long, but scrubbing any algae from the sides of the pool can take hours. So, keeping the pH and chlorine right takes periodic checking to avoid having algae.
Handing it off to a pool service, once you failed a couple of times, is what often happens. They charge anywhere from $100 to $200 a month, some including chemicals, some without. You have to negotiate.