TL;DR: What is the proper way of calculating the exact loss (due to the exchange rate(*)) on a currency exchange transaction?
(*) I'm not interested in other costs, like commission fee.
Longer example: AKA what I assume is the 'proper' way:
Let's say I'm a tourist in the EU and I want to buy
100 EUR for
USD. I check the official exchange rate, which today (26.12.2018, according to Google) is
1 EUR = 1.139 USD. Let's assume this is the 'official' exchange rate, and work with this.
Now, if I find a place that sells me
1 EUR for
1.2 USD and I buy
100 EUR, then I will spend
1.2 * 100 = 120 USD. But, if I could have bought the
100 EUR for the official rate, I would have spent only
1.139 * 100 = 113.9 USD.
So, on the transaction, I have lost
120 - 113.9 = 6.1 USD which is
6.1 / 1.139 = 5.36 EUR.
Question: is the above calculation correct? If not, then what are the issues, and what would be the correct way to calculate the loss?