Hello,
Firstly welcome to AM. Airline Mogul is running 24 hours a day, so while you are offline or away from AM you are still earning money. You don't need to keep the game open either. Watch out for the month change, which occurs at the 24th of each month. Gate costs and other monthly expenses (Such as leases and maintenance) are deducted. This may be the reason why there was little change in your cash, as expenses were taken out and then income added for the period.
I hope this helps.
