# Is there a difference between buying a currency and selling the currency to be converted to?

I'm not an economist. I'm looking to exchange my CAD to EUR. I watched the rates on a exchange office, and I found something strange:

We buy:                   We sell:
1 EUR = 1,4946 CAD (1)    1 EUR = 1,3280 CAD (2)
1 CAD = 0,6691 EUR (3)    1 CAD = 0,7530 EUR (4)


How can there be 4 different rates? I understand why CAD -> EUR is different of EUR -> CAD with the supply and demand. When the exchange office buys 1 CAD, it sells EUR too. I supposed it was to make things easier, so I checked it:

1 EUR = 1,3280 CAD (2)
=> 1,3280 CAD = 1 EUR

1 CAD = 0,6691 EUR (3)
1,3280 * 1 CAD = 1,3280 * 0,6691 EUR
=> 1,3280 CAD = 0.8886 EUR


Here, we found that it's indeed, more interesting for the customer to accept a sell than buying (from the office point of view for the words buy/sell). But is the difference, normal? And why?

Buy and sell rates are different because the currency vendor wants to make a profit and is also taking some risk with the exchange. It is possible that she cannot unload all the CADs they buy from you immediately and then perhaps in the future they will depreciate. (Perhaps they will appreciate. It is uncertain, hence there is risk.)

The same applies to buying and selling euros.

Usually there is some middle rate $x$ EUR/CAD. The vendor will deviate 1-2% from this in the direction favorable to her, depending on the direction of the deal (buying EURs with CAD or the other way around). You can look up something close the middle rate on XE. Currently this is about 1.394 CAD/EUR. Your vendor seems to sell at a premium that seems higher than normal to me, so perhaps see if you can find another currency merchant.

There are in fact two rates (subject to minor rounding), each expressed two different ways (a rate and its reciprocal), presumably to help different people who think different ways.

Suppose you wanted to buy $1000$ Euros with Canadian dollars. The calculation is either $1000\times 1.4946 = 1494.60$ or $\dfrac{1000}{0.6691}=1494.54$ - the same within six cents

Similarly if you want to sell $1000$ Euros for Canadian dollars. The calculation is either $1000\times 1.3280 = 1328.00$ or $\dfrac{1000}{0.7530}=1328.02$ - the same within a couple of cents

The gap between the rates in the two directions (a gap of over $160$ dollars for $1000$ Euros) is much more than the handful of cents when using a particular rate or its reciprocal