Stacy is correct.

Latest (Jun 27) official exchange rate:

Each Euro costs $1.1423 + whatever your bank or money exchanger tacks onto the cost, usually about 1 1/2%, if you buy in quantity like 5,000 Euros. So Friday one Euro would cost a minimum of $1.16.

You mentioned the bank you called offered to give you $1.02 for each Euro. It doesn't mean that you would pay $1.02 per Euro - it means you would only receive $1.02 for each Euro you sell instead of the official rate of $1.14.

In my experience airports and hotels are the worst places to exchange money.