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Given the following, is there a profitable arbitrage opportunity and, if so, how much money can...

Given the following, is there a profitable arbitrage opportunity and, if so, how much money can you make per dollar arbitraged?

Brussels 0.68 pounds = $1
US $1.42 = 1 Euro
London 1 Euro = 0.91 pounds

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Answer #1

Cross currency rate

1 USD = 0.68 pounds and

1 USD = 1 / 1.42 Euros

i.e. 1 USD = 0.7042 Euros

Therefore

0.7042 Euros = 0.68 pounds

Therefore 1 Euro = 0.68/0.7042 pounds

Therefore 1 Euro = 0.9656 pounds

Since direct exchange rate between Euro - pound is not equal to cross currency exchange rate derived, there is arbitrage opportunity.

Since Euros are cheaper to buy directly in pounds compared to cross currency buying, we will buy Euros directly though pounds

Arbitrage per dollar:

Convert 1 USD to 0.68 pounds

Use 0.68 pounds to buy Euros, that is 0.68 / 0.91 = 0.7473 Euros

Convert 0.7473 Euros to USD @ 1.42

Therefore 0.7473 Euros = 1.0611 USD

Therefore 1 USD got converted to 1.0611 USD.

Therefore arbitrage gain per USD = 0.0611 USD

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