I JUST HAVE RENTED A HOUSE WITH AN ATTIC FAN AND WAS WONDERING HOW MUCH IT WOULD SAVE ME ON THE ENERGY BILL?

Without specific numbers (attic fan horsepower, air conditioner efficiency and size) it will still be a very round number, but I’ll give you a guess.
If your house is average size (about 1600 sq ft maybe?) your AC unit is likely about 3 tons (this depends on your house insulation). If the unit is relatively new, the efficiency should be 13 SEER and might draw around 3.5 kW while running. Your attic fan, however, draws much less than that. It could be 1/3 hp or 1.5 hp…but hopefully around 1/2hp (about 325 W)
More guesswork: You run the attic fan for 8 hours then close up the house for the day. You run the AC for 1 hour/day. Running only the AC equates to maybe 5 hours of total peak running.
Now:
5 hours x 3.5kW = 17.5 kWH/day for AC
8 hours x .325kW + 1 hour x 3.5kW = 6.1 kWH/day for fan/AC
So you might save around 11kWH per day and 330kWH per month.
If you pay 12 cents per kWH it could mean $40/mo.
Again, this is VERY round numbers, but you will definitely save dollars per month, not just cents.
Remember, also, that this might not compare well with your apartment, as the AC there might have been much smaller.