# How to Calculate an Exchange Rate

An exchange rate is how much it costs to exchange one currency for another. Exchange rates fluctuate constantly throughout the week as currencies are actively traded. This pushes the price up and down, similar to other assets such as gold or stocks. The market price of a currency—how many U.S. dollars it takes to buy a Canadian dollar for example—is different than the rate you will receive from your bank when you exchange currency. It is often a key element of financial trilemmas. Here's how exchange rates work, and how to figure out if you are getting a good deal.

## Finding Market Exchange Rates

Traders and institutions buy and sell currencies 24 hours a day during the week. For a trade to occur, one currency must be exchanged for another. To buy British Pounds (GBP), another currency must be used to buy it. Whatever currency is used will create a currency pair. If U.S. dollars (USD) are used to buy GBP, the exchange rate is for the GBP/USD pair. Access to these forex markets can be found through any of the major forex brokers.

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#### How To Calculate An Exchange Rate

If the USD/CAD currency pair is 1.33, that means it costs 1.33 Canadian dollars for 1 U.S. dollar. In USD/CAD, the first currency listed (USD) always stands for one unit of that currency; the exchange rate shows how much of the second currency (CAD) is needed to purchase that one unit of the first (USD).

This rate tells you how much it costs to buy one U.S. dollar using Canadian dollars. To find out how much it costs to buy one Canadian dollar using U.S. dollars, use the following formula: 1/exchange rate.

In this case, 1 / 1.33 = 0.7518. It costs 0.7518 U.S. dollars to buy one Canadian dollar. This price would be reflected by the CAD/USD pair; notice the position of the currencies has switched.

Some of the most popular currencies that trade against the greenback are the Euro (EUR/USD), the Japanese Yen (USD/JPY), the British Pound (GBP/USD), the Swiss Franc (USD/CHF), the Australian Dollar (USD/AUD), the New Zealand Dollar (USD/NZD), and the Canadian dollar (USD/CAD). Incidentally, the ordering in each set of parentheses reflects the customary direct quote scheme for each pairing.

When you go to the bank to convert currencies, you most likely won't get the market price that traders get. The bank or currency exchange house will markup the price so they make a profit, as will credit cards and payment services providers such as PayPal, when a currency conversion occurs.

If the USD/CAD price is 1.33, the market is saying it costs 1.33 Canadian dollars to buy 1 U.S. dollar. At the bank though, it may cost 1.37 Canadian dollars. The difference between the market exchange rate and the exchange rate they charge is their profit. To calculate the percentage discrepancy, take the difference between the two exchange rates, and divide it by the market exchange rate: 1.37 - 1.33 = 0.04/1.33 = 0.03. Multiply by 100 to get the percentage markup: 0.03 x 100 = 3%.

A markup will also be present if converting U.S. dollars to Canadian dollars. If the CAD/USD exchange rate is 0.75 (see the section above), then the bank may charge 0.7725. They are charging you more U.S. dollars than the market rate. 0.7725 - 0.75 = 0.0225/0.75 = 0.03 x 100 = 3% markup.

Banks and currency exchanges compensate themselves for this service. The bank gives you cash, whereas traders in the market do not deal in cash. In order to get cash, wire fees and processing or withdrawal fees would be applied to a forex account in case the investor needs the money physically. For most people looking for currency conversion, getting cash instantly and without fees, but paying a markup, is a worthwhile compromise.

Shop around for an exchange rate that is closer to the market exchange rate; it can save you money. Some banks have ATM network alliances worldwide, offering customers a more favorable exchange rate when they withdraw funds from allied banks.

Need a foreign currency? Use exchange rates to determine how much foreign currency you want, and how much of your local currency you'll need to buy it.

If heading to Europe you'll need euros (EUR), and will need to check the EUR/USD exchange rate at your bank. The market rate may be 1.113, but an exchange might charge you 1.146 or more.

Assume you have $1,000 USD to buy Euros with. Divide$1,000 by 1.146 (what a bank may charge) to get 872.60 euros. That is how many Euros you get for your \$1,000. Since Euros are more expensive, we know we have to divide, so that we end up with fewer units of EUR than units of USD.

Now assume you want 1,500 euros, and want to know what it costs in USD. Multiply 1,500 by 1.146 to get 1,719 USD. Since we know Euros are more expensive, one euro will cost more than one US dollar, that is why we multiply in this case.

## The Bottom Line

Exchange rates always apply to the cost of one currency relative to another. The order in which the pair are listed (USD/CAD versus CAD/USD) matters. Remember the first currency is always equal to one unit and the second currency is how much of that second currency it takes to buy one unit of the first currency. From there you can calculate your conversion requirements. Banks will markup the price of currencies to compensate themselves for the service. Shopping around may save you some money as some companies will have a smaller markup, relative to the market exchange rate, than others.

Article Sources
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1. Bank for International Settlements (BIS). "Triennial Central Bank Survey Foreign Exchange Turnover in April 2019 Monetary and Economic Department," Pages 5, 10.

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