Question

You just came back from Canada, where the Canadian dollar was worth $.70. You still have C$500 from your trip and could exchange them for dollars at the airport, but the airport foreign exchange desk will only buy them for $.90. Next week, you will be going to Mexico and will need pesos. The airport foreign exchange desk will sell you pesos for $.20 per peso. You met a tourist at the airport who is from Mexico and is on his way to Canada. He is willing to buy your C$500 for 900 pesos. Should you accept the offer or cash the Canadian dollars in at the airport?

1. What is the cross rate of the Peso per Canadian dollar at the airport foreign exchange desk?
2. What is the cross rate of the Peso per Canadian dollar offered by the tourist?
3. Should you accept the offer from the tourist or at the airport?

Answer 1

The airport exchange has given the following quotations-

$/C$ = 0.9

And $/peso = 0.2

We know that when we have quotation A/B = C where A is the price currency and B is the base  currency. The B/C will be 1/C and also A/B * B/C will be A/C

Using this we will calculate the cross rate

Now, C$/$ * $/Pepso = (1/0.9) * (0.2) = 0.2222

Hence C$/Pepso = 0.2222

This is the cross rate in airport

Now we will calculate tour cross rates

Given tourist is willing to buy C$ 500 for 900 pepso

That means his quotation can be interpreted as C$/Pepso is 500/900

C$ per pepso = 0.55555

This is the cross rate with the tourist

Let us interpret both the rates

For buying 1 pepso in airport we will cost 0.22222 C$ where as from tourist it will cost 0.5555C$

Hence it is better to exchange in the airport itself