Unit 6 · Topic 6.2

Exchange Rates

An exchange rate is the price of one currency in another, and it can be written two ways that are reciprocals of each other.

Practice 1: Principles and Models

Part 1 · Hook

Why this matters

A student in Chicago is saving for a summer in Spain. The rent there is set in euros, but her savings are in dollars, so one number decides how far her money goes: how many dollars it takes to buy one euro. When that number moves, her summer gets cheaper or dearer without any price in Spain changing.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. A US tourist pays for a hotel in Spain. How does the balance of payments record it?

  1. As an import of services, a debit in the US current account
  2. As a credit in the US capital and financial account
  3. As an export of services by the United States
  4. It is not recorded, since no asset is bought
Show the answer

Money leaves the US to pay for a service bought abroad: an import of services, a current account debit.

  • Correct: As an import of services, a debit in the US current account:
  • As a credit in the US capital and financial account:
  • As an export of services by the United States:
  • It is not recorded, since no asset is bought:

2. Which function of money lets you compare the prices of two things, such as a jacket and a phone?

  1. Unit of account
  2. Store of value
  3. Medium of exchange
  4. Legal tender
Show the answer

A unit of account is a common measure of value. An exchange rate lets you compare prices set in two different units.

  • Correct: Unit of account:
  • Store of value:
  • Medium of exchange:
  • Legal tender:

Part 4 · See it

See it first

Suppose 1 euro equals 1.25 dollars; flipped, 1 dollar equals 0.80 euro, because 1 divided by 1.25 is 0.80. When the rate changes to 1 euro equals 1.50 dollars, the euro appreciates (it buys more dollars, and a 40-euro ticket costs 60 dollars instead of 50) and the dollar depreciates (it buys about 0.67 euro instead of 0.80). Made-up rates for practice.
One rate written two ways (1.25 dollars per euro is 0.80 euro per dollar). When a euro buys more dollars, the euro appreciates and the dollar depreciates. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. The price of a euro rises from 1.25 dollars to 1.50 dollarseach euro buys more dollars: the euro appreciates
  2. Each euro buys more dollarseach dollar buys fewer euros (0.80 to about 0.67): the dollar depreciates
  3. The dollar depreciates against the eurogoods priced in euros cost Americans more dollars, and goods priced in dollars cost Europeans fewer euros

Part 6 · Key ideas

Key ideas

  • An exchange rate is the price of one currency in units of another: "1.25 dollars per euro" is the price of one euro.
  • The same rate can be written either way; one quote is the reciprocal of the other: 1.25 dollars per euro is 11.25=0.80\frac{1}{1.25} = 0.80 euro per dollar.
  • A currency appreciates when one unit buys more of the other currency, and depreciates when it buys less. When one currency appreciates, the other depreciates.
  • To convert a price, multiply it by a rate whose units cancel: euros times dollars per euro gives dollars.

Part 7 · Misconception

A common mistake

The wrong idea: A bigger number in an exchange rate quote always means that currency got stronger.

What actually happens: It depends on the units. In "dollars per euro", a bigger number means the euro appreciated and the dollar depreciated. Flip the quote to euros per dollar and the same change makes the number smaller.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data

The price of the arl in bels

Bels per arl at the start of each year (invented data for practice; the arl is the currency of Arland, the bel the currency of Belvia)
YearBels per arl
12.0
22.5
31.6

1. Use the table. In Year 2, what is the price of one bel in arls (arls per bel)?

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

The table gives bels per arl. Flip it: 12.5=0.4\frac{1}{2.5} = 0.4 arls per bel. One arl buys 2.5 bels, so one bel buys 0.4 of an arl.

  • Answer: 0.4

2. Use the table. What happened from Year 1 to Year 2?

  1. The arl appreciated and the bel depreciated
  2. The arl depreciated and the bel appreciated
  3. Both currencies appreciated
  4. Neither changed in value, since prices did not change
Show the answer

More bels per arl: the arl appreciated and the bel depreciated.

  • Correct: The arl appreciated and the bel depreciated: Right: one arl bought 2.0 bels and then 2.5 bels, so the arl buys more bels (it appreciated) and each bel buys less of an arl (it depreciated).
  • The arl depreciated and the bel appreciated: The quote is bels per arl, so a higher number means each arl buys more bels: the arl gained value.
  • Both currencies appreciated: When one currency buys more of the other, the other buys less of the first: one appreciates as the other depreciates.
  • Neither changed in value, since prices did not change: The exchange rate itself changed, from 2.0 to 2.5 bels per arl; that is a change in the value of each currency against the other.

3. Use the table. In Year 3, a hotel in Belvia charges 300 bels a night. What does one night cost an Arland traveler, in arls?

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

Turn the rate into arls per bel, 11.6=0.625\frac{1}{1.6} = 0.625, then multiply: 300×0.625=187.5300 \times 0.625 = 187.5 arls. Check the units: bels times arls per bel gives arls.

  • Answer: 187.5

4. What is an exchange rate?

  1. The interest rate a central bank pays on reserves
  2. The price of one currency in units of another
  3. A country's exports divided by its imports
  4. The gap between two countries' inflation rates
Show the answer

An exchange rate is the price of one currency expressed in units of another currency.

  • The interest rate a central bank pays on reserves: That is an administered interest rate of a central bank, not the price of a currency.
  • Correct: The price of one currency in units of another: Right: for example, the number of dollars one euro costs, or the number of euros one dollar costs.
  • A country's exports divided by its imports: That ratio compares trade flows; an exchange rate is a price of money in terms of other money.
  • The gap between two countries' inflation rates: Inflation differences can move exchange rates, but an exchange rate is the price of one currency in another.

5. A rate quoted as arls per bel rises from 0.40 to 0.50. What happened?

  1. The arl appreciated against the bel
  2. The bel depreciated against the arl
  3. Nothing can be said without a quote in bels per arl
  4. The bel appreciated against the arl
Show the answer

Arls per bel is the price of the bel; a higher price means the bel appreciated.

  • The arl appreciated against the bel: It now takes more arls to buy one bel, so each arl is worth less: the arl depreciated.
  • The bel depreciated against the arl: One bel now buys 0.50 arl instead of 0.40, which is more, so the bel gained value.
  • Nothing can be said without a quote in bels per arl: One quote is enough: the other is its reciprocal, so a rise in arls per bel is a fall in bels per arl.
  • Correct: The bel appreciated against the arl: Right: the quote is the price of a bel in arls, and that price rose, so the bel appreciated (and the arl depreciated).

6. A concert ticket in Arland costs 60 arls. The exchange rate is 1.5 bels per arl. What does the ticket cost a visitor from Belvia, in bels?

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

Multiply the arl price by bels per arl: 60×1.5=9060 \times 1.5 = 90 bels. Units check: arls times bels per arl gives bels.

  • Answer: 90

Part 9 · Summary

Summary

An exchange rate is the price of one currency in another, and it can be written two ways that are reciprocals of each other. When one unit of a currency buys more of the other currency, it has appreciated, and the other has depreciated by the same change. Read the units before you compare two rates or convert a price: the units tell you which currency the number is the price of.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

Question set for this topic