Exchange Rates: Introduction: Videos & Practice Problems

Exchange rates represent the value of one currency in terms of another, calculated as a ratio. For example, if $1 equals €0.93, this means for each US dollar, you receive €0.93. Conversely, €1 would yield $1.07. Understanding these ratios is crucial for analyzing currency values and making informed financial decisions in the foreign exchange market. The interpretation of these ratios helps in grasping concepts like appreciation and depreciation of currencies, which are vital in macroeconomic contexts such as balance of payments and aggregate demand management.

Exchange Rates: Introduction

So if you've ever traveled to a foreign country, you had to exchange your dollars for a foreign currency. Let's learn a little bit more about these exchange rates. So $1 does not equal €1, does not equal €1, does not equal 1 rupee, does not equal any other currency, right? We have to exchange our dollars for other currencies based on the exchange rate. So the exchange rate determines how much of a foreign currency you can get for your domestic currency, say your US dollars, right? US dollars. So exchange rates are basically a ratio. So the ratios between the values of 2 currencies, okay? And we're going to learn a little bit more of how to examine an exchange rate because this can generally be a kind of confusing topic when it comes to doing some math here.

So when we talk about ratios, we're always going to divide one number by another number. That's how we do a ratio. We're going to take a number, divide it by another number and that's going to tell us. Okay? So it's important to be able to calculate the ratio, but also important to be able to analyze the results. What does it mean when we get the answer to the ratio?

So first, let's start with a generic ratio interpretation and then we'll apply it to currency exchanges here. So ratio, like I said, we're dividing one number by another. So it's going to be a divided by b. And this is generally going to be when we talk about it, different currencies. The amount of a foreign currency divided by the amount of dollars, something like that. So when we interpret a ratio, we're going to do the division and say that this division gave us 1.54, right? Like I have in my example. Let me do it in another color here. 1.54, right?

So how do we interpret this ratio? Well, we calculate the ratio by doing the division and then what this tells us, this 1.54, it would tell us that for each unit of B, the denominator. So if the denominator was US dollars, for each US dollar, we would get 1.54 units of A, whatever the foreign currency is. Let's say €1.54 per US dollar, something like that, okay? So that's how we interpret it because anytime you do a division, A divided by B, you do that in your calculator, you get 1.54. Well, that's the same thing as 1.54 A divided by 1 B, right? For every 1 unit of B, you'll have 1.54 units of A.

So when we apply this to exchange rates, it's just going to be currency 1 divided by currency 2, right? And that's our ratio, AB, currency 1 divided by currency 2. Now, there are 2 ways to explain the same exchange rate, right? We could say how many euros per US dollar or how many US dollars per euro, okay?

Now, it gives us the same answer in either case. So for example, if 1 US dollar is worth €0.93, well, we can do this. We can do €0.93 divided by $1.00 and that tells us 0.93, right? 0.93 divided by 1 is €0.93 per dollar. So if you were to give them, you go to the bank and you say, hey, I want to exchange this to euros, they'll give you €0.93 back. Okay? So each $1 will get you €0.93.

Now, we could say the same thing because what if we had €1 and wanted to do 1 divided by €0.93. And this is the same thing because they are equal to each other, right? So we're able to flip it and it still gives us a ratio, but the interpretation is a little different. So let's get our calculator out and let's do this. 1 divided by 0.93 gives us approximately 1.07, 10.93 American money, they'll give you $1.07. Okay? And that's because of this exchange rate. If we had a different exchange rate, we would get different numbers here, okay? So notice how we're analyzing this ratio. We did 1 divided by 0.93, and the calculator said 1.07 when we did that. But we have to know what does that mean. That means 1.07 of the top per one of the bottom, right? Just like we said in our ratio interpretation. That means for each one unit of B, the bottom, there are 1.54 units of A, the top, right? So that's how we calculate how we interpret a ratio. Whenever we put it in the calculator, it's always this amount of the top currency divided for each one of the bottom.

Exchange Rates

Alright. So let's try this example together. But before we get into it, I want to teach you a little trick about exchange rates that comes into play with any kind of unit conversion. So let's do a simple example before we get to this one where we're going to think about we have we know our exchange of feet to inches, right? We know that there are 12 inches per foot, right? Per 1 foot, which is the same thing as for every 1 foot, there's 12 inches, right? So if I were to ask you, how many inches are in 3 feet? Well, you would probably know that there are 36 inches right? 12 inches per 1 foot, 3 feet, 36 inches right? Well, how do we use this and show it mathematically? Okay. So this is technically our exchange rate here. 12 inches for every 1 foot or 1 foot for every 12 inches, right? And we want to know 3 feet, how many inches, right? 3 feet, how many inches? So the idea is we're going to use our exchange rate from inches to feet and we're going to multiply it by feet. The idea is that we want to in 3 feet? How many inches for in 3 feet? How many inches in 3 feet? So we want to cancel out the units of feet and be left with inches. Let me show you what I mean. So we're going to use our exchange rate, 12 inches for 1 foot, and we're going to multiply it by how many feet we want. We want 3 feet. So in 3 feet, how many inches are there? And what can happen here is we can cancel out these units. So notice that the feet are in the numerator here because it's 3 over 1, right? There are 3 and then there are feet in the denominator. So from a mathematical standpoint, we can cancel out those units, the feet and the feet and we'll be left with inches. This is the way I want you to think about doing these currency exchanges when you have to do math like we see in this problem. So 12 divided by 1 times 3. So now, we use the numbers. We've canceled out the units and we're left with inches. 12 divided by 1 is 12 times 3 is 36 inches right? So that tells us that in 3 feet, there's 36 inches right? If there's 12 inches per foot, 3 feet, well, that gets us to 36 inches So what you want to do is be able to cancel out the feet. Notice, if we had used this if we had used this one right here, 1 foot divided by 12 inches we would not be able to cancel out because feet would have both been in the numerator. We want to cancel out feet and feet here. So this does not work. We want to use this one right here. Okay? So you want to think, we can always flip the exchange rate so that we can cancel out the units that we don't want and end up in the units we do want. Okay? So now let's look at our actual example here. Clutchtopia's currency conversion is currently 1.7 Clutch coin for 1 US dollar. 1.7 Clutch coin cc's per 1 US dollar. So there's our exchange rate. If a US citizen was planning to visit Clutchtopia, how many dollars? So let me erase this right here. How many dollars would they need, right? How many dollars? So we want our final answer to be in dollars, right? So we want to cancel out the clutch coins and be left with dollars. How many dollars would they need to exchange to receive 100 clutch coins? So what we need to do is convert these units from Clutch Coins to Dollars. And we're given our 2 exchange rates here. So I don't want to leave this empty. This was what it was over here before. Okay, what are our two exchange rates that are equivalent to each other? We either have 1.7 clutch coins per 1 US dollar or 1 US dollar per 1.7 clutch coin, and we want to do the same thing. Do we want to end up in dollars, or do we want to end up in clutch coins? What is our question asking us? It's asking us how many dollars, right? So we want to end up in dollars, we want to cancel out the clutch coin. So what we need is clutch coin in the denominator and clutch coin in the numerator to cancel out. Just like we had in our example over here. So what are we going to do? We're going to use this one that has clutch coins in the denominator because we're going to multiply it by 100 clutch coins. We want to know how many dollars are needed to receive 100 clutch coins. So we want to go in the bank with a certain amount of dollars and then leave the bank with 100 clutch coins. So how many dollars is that? So what we're going to do, we're going to do the 1.1 US dollar divided by 1.7 clutch coins, and we're going to multiply it by the 100 clutch coins. Right? We multiply it by 100 because this exchange rate is equal to 1. That's what 1 would be. So we multiply it by the 100 clutch coins and we'll see how many dollars it would be. So notice what happens. We've got clutch coins in the denominator, clutch coins in the numerator and the clutch coins are gone, and we're left with US dollars. Okay? So what we need to do is 1 divided by 1.7, so now we do the math. 1 divided by 1.7 times 100 and that gives us that equals 58.82. 58.82 and that's in dollars, right? That gives us an amount in dollars because we've canceled out these clutch coins here and we're left with US dollars. Okay? So that's what this tells us here. It tells us the amount of US dollars"],["we need to get 100 clutch coins. Okay? So I know it can be a little tricky when it comes to exchange rates, but being able to do this unit conversion and flipping the exchange rate when you need to to cancel out the units, that's a big trick in being able to solve these exchange rate problems. Alright. Let's pause here and now you guys can try a practice simulation.

Clutchtopia currently exchanges 0.8 ClutchCoin (CC) for 1 US dollar (USD). If a ClutchBurger costs 3.50 CC, what is the USD equivalent price for a ClutchBurger?

Alright. Let's see how you guys did here. Clutchtopia currently exchanges 0.8 Clutch coin for 1 US dollar. So there is our exchange rate, 0.8 Clutch coin per 1 US dollar. If a clutch burger costs $3 or 3.5 Clutch coins, what is the US dollar equivalent price for a clutch burger? So we want US dollars, right? We want the US dollar equivalent price of a clutch burger. We know a clutch burger costs 3.50 Clutch coins and we know the exchange rate. So how many US dollars do we need? There are two ways to show this exchange rate: 0.8 Clutch coin per 1 US dollar or 1 US dollar for 0.8 Clutch coin, right? They both mean the same thing. Which one is going to be important to us here? We want to end up in US dollars, right? So we want to get rid of the Clutch coins by canceling out the units in the denominator and the numerator. Okay? So what we know is 1 US dollar for 0.8 Clutch coin. So what we're going to do is we're going to use 1 US dollar divided by 0.8 Clutch coin and we're going to multiply it by how many Clutch coins we need. We need 3.5 Clutch coins, right? And now, this cancels the Clutch coin here, and here, and we'll be left with our final answer in US dollars, right? Our final answer in US dollars. So what we do is we do 1 0.8 times 3.5 and it gives us approximately $4.38. We'll need $4.38 American money to get 3.5 Clutch coins and buy this clutch burger, okay? So notice what we did again. We used our exchange rate. We could use either one. They both mean the same thing, but we want to use the one that allows us to cancel the Clutch coins. So what is the interpretation of this? $1 divided by 0.8 Clutch Coins. So this right here, when we do so, let me use this one up here. When we do this right here, 1 0.8 , it gives us 1.25. And remember how we said we would interpret ratios. For each one of the denominator, for each one Clutch coin, we would need 1.25 US dollars, okay? So 1.25 US dollars for each Clutch coin, we need 3.5 Clutch coins. So 1.25 times the 3.5 Clutch coins we need equals our final price, $4.38. Okay? So that's how we interpret the ratio. Clutch coin, each one of the denominator requires 1.25 of the numerator. 1.25 US dollars per Clutch coin or per 1 Clutch coin, okay? So that's the interpretation there. The final answer, $4.38 for that clutch burger. Alright, let's go ahead and move on to the next.

Here’s what students ask on this topic:

What is an exchange rate and how is it calculated?

An exchange rate represents the value of one currency in terms of another. It is calculated as a ratio of the two currencies. For example, if $1 equals €0.93, the exchange rate is 0.93. This means for each US dollar, you receive €0.93. Conversely, to find how many US dollars you get for €1, you divide 1 by 0.93, resulting in approximately $1.07. Understanding these ratios is crucial for analyzing currency values and making informed financial decisions in the foreign exchange market.

How do you interpret an exchange rate ratio?

To interpret an exchange rate ratio, you divide one currency by another. For instance, if the exchange rate is 1 USD = 0.93 EUR, you interpret this as for every 1 US dollar, you get 0.93 euros. Conversely, if you want to know how many US dollars you get for 1 euro, you divide 1 by 0.93, resulting in approximately 1.07 USD. This means for each euro, you receive $1.07. Understanding this helps in grasping concepts like currency appreciation and depreciation.

Why are exchange rates important in macroeconomics?

Exchange rates are crucial in macroeconomics because they affect international trade, investment, and economic stability. They influence the cost of imports and exports, impacting a country's trade balance. Exchange rates also affect inflation and interest rates, which are vital for aggregate demand management. Additionally, they play a role in the balance of payments, determining how much foreign currency is needed to pay for goods and services from abroad. Understanding exchange rates helps policymakers and businesses make informed decisions.

What factors influence exchange rates?

Several factors influence exchange rates, including interest rates, inflation, political stability, economic performance, and market speculation. Higher interest rates offer lenders a better return relative to other countries, attracting foreign capital and causing the currency to appreciate. Low inflation rates typically lead to a currency appreciation, as purchasing power increases. Political stability and strong economic performance make a country more attractive to foreign investors, boosting the currency's value. Market speculation can also cause fluctuations as traders react to news and economic indicators.

How do exchange rates affect international trade?

Exchange rates significantly impact international trade by influencing the cost of exporting and importing goods and services. A stronger domestic currency makes exports more expensive and imports cheaper, potentially reducing export volumes and increasing imports. Conversely, a weaker domestic currency makes exports cheaper and imports more expensive, boosting export volumes and reducing imports. These changes affect a country's trade balance, economic growth, and employment levels. Understanding exchange rates helps businesses and policymakers navigate the complexities of international trade.