The Fair Value of Paying in Currency X for Goods Bought in Currency Y

Me and my friends are from Europe, we went to US. At the end of the trip they bought an item worth $USD 100$, but because they were short of money, so I paid for the item first with my own $USD 100$.

After we came back from Europe, they would have to pay me. They would like to pay me in EUR. What is the fair amount of EUR they should pay me?

Assuming that at money exchange counter, the rates are as follow ( buy/sell are from their perspective):

1 EUR buys $\frac{1}{1.05}$ USD.

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A 500 pip spread on EURUSD? – barrycarter Apr 6 '11 at 15:30
In exchange booths at many airports it can be even worse. – finitud Apr 12 '11 at 18:29

Not realy a quant question but funny though,

Here are my two euro-cents,

I would say that you should ask them for 100-USD times the exchange rate at the date you lend them, plus the interest rates amount that can be calculated by compounding EUR EONIA rate on the period you lend them that money.

Regards

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This is just a no-arbitrage argument: whatever you paid for the 100 USD plus the corresponding interest rate.

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But the problem is that if they insist on paying me in EURO, how much should I charge them? 100 EUR? or 105 EUR? – Graviton Apr 12 '11 at 8:54
If you bought USD with EUR, the exchange rate you paid fixes the price. But it would be useful to know what your numeraire is... are you USD or EUR based? – finitud Apr 12 '11 at 10:03
EUR based. As mentioned in the question – Graviton Apr 12 '11 at 10:57