In situations where a A/C unit is old, it struggles to cool the house down.
Mainly on summer afternoons, when the temperatures outside is the hottest!
When you upgrade to a newer efficient unit, you will have a better unit to help stabilize the temperatures as they rise in the afternoon and will help on the cost of running the unit.
Don't turn up your thermostat when you are not home. This only makes your air conditioner work harder to cool the house down. It has to pull heat from carpet, walls, furniture etc.. before the air gets cooler.