Can a water leak increase my electricity bill?

ABSOLUTELY. When hot water goes down the drain, cold water replaces the used hot water in your water heater tank. Then, the heating Cycle begins to heat up the cold water. If you have well water, you also have a well pump that is constantly cycling to fill the water tank to replenish the leaking water supply.

FIX IT! The sooner, the better. You have already wasted a minimum of $ 58.00 you could have used toward your plumbing repair bill.

TURN your hot water supply OFF when you are not home, when you are asleep and when no one is using it...until it is repaired. 

Yes.  If you have well water it will make your pump run more often, resulting in more electricity usage.  And if it's hot water that's leaking and you have an electric water heater, it will run more often as it heats up the cold water slowly going into the tank.  You need to get that faucet replaced, or at least replace the seals in it.

Sure, it will increase your electricity bill if your supply system depends on the electricity.

Well, your usual response to all the problems you make for yourself is to have another baby, so . . . . . . 

maybe it leaking to put out the electrical fire !!! how about just changing the washers , then yu wont have a leak .. amazing how they dont know whats a plumber for !!!!

the problem is if you don't understand plumbing the next plumber will rip you off

If you heat your watr with electricity it can, yes.

leaking hot water runs the water heater, so yes -- this can increase your electric bill.  my guess, offhand, is that most of the increase is home heating, not the leaking water.  still, i'd fix it anyway -- take photo of the whole, write down the brand, and go to the home improvement store -- the salesman will help you find what parts you need.  It's a handyman job, not a plumber job, and thus ripe for DIY-- grampa

If your projected monthly bill is $300, your projected weekly bill is $75. You say you have accumulated $58 in the last week. That is BELOW $75.

" it's hot water."  <<<  Since you don't have gas, your water is heated by electricity.  This is no different than leaving your window open while the heater is on.  (Different costs, I'm sure, but still the same concept.)