Economics · Lesson e05

Exchange Rates: Money Across Borders

Every time you cross a border, the price of your pocket money changes. Here is how to read the rate, convert both ways and spot a real bargain.

A girl with a backpack holding coins and banknotes from different countries beside a currency exchange stall and a suitcase with travel stickers

When Mia travels, euros do not work in Mexico, and pesos do not work in Japan. To buy anything, she must exchange one currency for another. The deal is set by an exchange rate: how much of one currency buys one unit of another. Once you understand the rate as a simple ratio, you can price a saddle in Miami against one in Berlin without guessing.

Important: every exchange rate in this lesson is invented and rounded so the arithmetic is friendly. Real rates change every day and differ from these figures. Assume these rates for the whole lesson: EUR 1 = USD 1.10, EUR 1 = MXN 20, USD 1 = JPY 150, GBP 1 = EUR 1.15.

💡 Big idea 1: A rate is a conversion factor

"EUR 1 = USD 1.10" is a ratio: for every 1 euro you hand over, you get 1.10 dollars. It works like a recipe scaled up or down (proportionality, Lesson 13). To change euros into dollars, multiply by 1.10. Every euro turns into 1.10 dollars, so the dollar number comes out bigger.

💡 Big idea 2: Going back means undoing the factor

To convert in the other direction, divide by the same rate (or multiply by its flipped version). A quick sense check: the currency that is worth more per unit always has the smaller number. One euro buys more than one dollar here, so the same price shows a smaller number in euros than in dollars. If your answer goes the wrong way, you multiplied when you should have divided.

Matching marks on the two lines show the same amount of value in two currencies. The invented rate keeps the arithmetic friendly.

💡 Big idea 3: Compare prices in one currency, and why rates move

To compare a price in Miami with one in Berlin, convert both into the same currency first. Comparing "95" with "90" tells you nothing when they are different money.

Why does a rate move? A currency is something people buy, so supply and demand (e02) apply. If more people want euros (tourists, buyers of European horses and cars), demand rises and the euro buys more dollars. If fewer people want euros, the euro buys fewer. The rate is simply the price of one currency measured in another.

Maths connection: This is proportionality from Lesson 13: a constant ratio, a multiplication to go one way and a division to come back. Percent change (used to describe a rate moving) is the same skill as in your percentage lessons. And "who is cheaper?" connects to e03, where money does its "measuring" job across borders.

Worked Examples

Worked Example 1: both directions

Mia lands in Mexico City with EUR 35. Later, she has MXN 460 left over. Use EUR 1 = MXN 20.

Euros to pesos (multiply): $35 \times 20 = 700$, so MXN 700. The peso number is bigger because each peso is worth little.

Pesos to euros (divide): $460 \div 20 = 23$, so EUR 23. The euro number is smaller, which matches the sense check.

Worked Example 2: a fair comparison

A hot chocolate costs USD 4.40 in New York and EUR 3.60 in Madrid. Which is cheaper? Use EUR 1 = USD 1.10.

Step 1, one currency: convert the dollar price to euros: $4.40 \div 1.10 = 4.00$, so EUR 4.00.

Step 2, compare: EUR 3.60 (Madrid) against EUR 4.00 (New York). Madrid is cheaper, by EUR 0.40.

Warm-Up

Problem 1

Mia exchanges EUR 60 for US dollars at EUR 1 = USD 1.10. Calculate how many dollars she receives.

more or fewer dollars per euro? multiply or divide? →
Problem 2

On the flight home, Mia has USD 44 left. Before calculating, predict whether her euro amount will be bigger or smaller than 44 and give a reason. Then calculate the amount in EUR.

predict → calculate → does it match? →
Problem 3

The rate is EUR 1 = MXN 20. Write the same exchange rate in the form MXN 1 = EUR ?.

flip the ratio →

Core Problems

Problem 4

Mia is flying to Tokyo from Madrid with EUR 50 to spend. Use EUR 1 = USD 1.10 and USD 1 = JPY 150. Calculate how many Japanese yen (JPY) her euros are worth.

EUR to USD first, then USD to JPY →
Problem 5

The same riding helmet costs USD 95 in Miami and EUR 90 in Berlin. Using EUR 1 = USD 1.10, decide which city is cheaper and by how many US dollars. (Be careful: 90 is smaller than 95, but those are different currencies.)

one currency, then compare →
Problem 6

Mia changes EUR 150 into pesos. The airport booth offers EUR 1 = MXN 18, and a city bank offers EUR 1 = MXN 20. Calculate how many more pesos she receives at the bank than at the booth.

two conversions, one difference →
Problem 7 Challenge

Last month EUR 1 = USD 1.10. This month EUR 1 = USD 1.21. (a) Calculate the percentage change in the dollar price of one euro. (b) Mia converts EUR 200 this month instead of last month. Calculate how many more dollars she receives. (c) State what must have happened to demand for euros, relative to supply, to push the rate up.

change ÷ original → compare two conversions → supply and demand (e02) →
Problem 8 Open

Imagine a huge wave of tourists decides to visit Japan this summer, and all of them need Japanese yen. Using supply and demand, explain what you expect to happen to the price of the yen in euros, who benefits and who loses (for example Japanese exporters, European tourists, Mia), and name one other real-world event that could shake an exchange rate. There is no single right answer, but your reasoning should be clear.

demand for yen → yen price → winners and losers →

Think like an economist 🧠 A "stronger" currency is not automatically better. A strong euro makes holidays abroad cheaper for you, but it makes European horses, cars and cheese more expensive for foreign buyers. Who would prefer a weaker euro, and why?

Show answers

Problem 1

USD 66 (60 × 1.10)

Problem 2

EUR 40 (44 ÷ 1.10). Prediction: smaller than 44, because one euro is worth more than one dollar, so fewer euros are needed.

Problem 3

MXN 1 = EUR 0.05 (1 ÷ 20)

Problem 4

JPY 8 250 (50 × 1.10 = USD 55, then 55 × 150)

Problem 5

Miami is cheaper, by USD 4 (Berlin helmet = 90 × 1.10 = USD 99, against USD 95)

Problem 6

MXN 300 (bank 150 × 20 = 3 000, booth 150 × 18 = 2 700)

Problem 7a

10% increase (0.11 ÷ 1.10)

Problem 7b

USD 22 more (200 × 1.21 = 242, against 200 × 1.10 = 220)

Problem 7c

Demand for euros rose (more people wanted to buy euros) and/or the supply of euros on offer fell, so the euro became more expensive in dollars.

Problem 8

Open. Look for: demand for yen rises, so the yen becomes more expensive in euros (the yen strengthens). Winners: those who hold or earn yen, such as people selling things in Japan for yen. Losers: European tourists, who must spend more euros per yen. The reasoning should link demand to price. Another event: interest rates changing, a war, a big export deal, or a crisis of confidence.

Next up → a new strand awaits You can now earn, budget, save, bank and convert across borders. Look out for the next economics lesson, where we use these tools to ask how whole countries trade and why prices around the world differ.

Exchange Rates: Money Across Borders

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