GM Lesson 018 Currency Exchange Rates

Learning Intentions

• Use currency exchange rates to convert between Australian dollars and foreign currencies.
• Calculate the value of money before and after currency conversion.
• Interpret exchange rate calculations in travel and purchasing contexts.

Prerequisites

• Understand that a rate compares two quantities with different units.
• Be able to multiply and divide decimals.
• Be able to round money amounts to two decimal places.
• Be able to interpret financial information in context.
• Be able to distinguish between Australian dollars and foreign currencies.

Key Idea Summary

Currency exchange rates tell us how much one currency is worth in another currency.

If the exchange rate is given as:

then:

and:

For example, if:

then every Australian dollar is worth US dollars.

Currency conversion problems often involve travel, online shopping, overseas prices, bank fees and comparison of costs between countries.

Direct Instruction and Worked Examples

Time Allocation

Time Allocation

Time Allocation

• Introduction, warmup and vocabulary: 5 minutes
• Direct instruction: 15 minutes
• Understanding checks: 5 minutes
• Exercises: 20 minutes
• Homework: 20 to 30 minutes outside the lesson it was taught in.

Link to original

Direct Instruction

An exchange rate is a rate comparing two currencies.

For this lesson, use the given exchange rate in each question. Real exchange rates change over time, so questions will provide the rate needed.

When converting from Australian dollars to a foreign currency, multiply by the exchange rate.

When converting from a foreign currency back to Australian dollars, divide by the exchange rate.

A useful way to remember the direction is:

• From AUD to many foreign units: multiply.
• From many foreign units back to AUD: divide.

Worked Example 1: Converting AUD to USD

A traveller exchanges $ Australian dollars into US dollars. The exchange rate is:

Calculate the amount received in US dollars.

The traveller receives:

Worked Example 2: Converting AUD to Japanese Yen

A student has $ Australian dollars for a trip to Japan. The exchange rate is:

Calculate the amount received in Japanese yen.

The student receives:

Worked Example 3: Converting Foreign Currency to AUD

A jacket costs EUR. The exchange rate is:

Calculate the cost of the jacket in Australian dollars.

Since the price is in EUR and the exchange rate tells us the value of AUD in EUR, divide by .

The jacket costs:

Worked Example 4: Including a Currency Exchange Fee

A bank charges a flat conversion fee of $ when converting Australian dollars into New Zealand dollars. Ava converts $ AUD. The exchange rate is:

Calculate the amount Ava receives after the fee is removed first.

First subtract the fee from the Australian dollars.

Now convert the remaining amount.

Ava receives:

Worked Example 5: Comparing Travel Costs

A hotel in Singapore costs SGD per night. The exchange rate is:

A similar hotel in Australia costs $ per night. Which hotel is cheaper in Australian dollars?

Convert the Singapore price into AUD.

Rounded to the nearest cent:

Compare:

The Australian hotel is cheaper by:

The Australian hotel is cheaper by $ per night.

Understanding Checks

Understanding Check 1

The exchange rate is:

A tourist exchanges $ AUD.

1. Should you multiply or divide?
2. Calculate the amount in USD.

Understanding Check 2

The exchange rate is:

A museum ticket costs EUR.

1. Should you multiply or divide to convert the cost to AUD?
2. Calculate the cost in AUD, rounded to the nearest cent.

Understanding Check 3

A bank gives the following exchange rate:

Mia converts $ AUD and pays a fee of $ before conversion.

1. How many Australian dollars are converted after the fee?
2. How many NZD does Mia receive?

Understanding Check 4

Explain why the following calculation is incorrect.

A watch costs USD. The exchange rate is:

A student calculates:

and concludes that the watch costs $ AUD.

Exercises

Simple Familiar Exercises

Exercise 1

Convert $ AUD to USD using the exchange rate:

Exercise 2

Convert $ AUD to EUR using the exchange rate:

Exercise 3

Convert $ AUD to JPY using the exchange rate:

Exercise 4

A meal costs USD. The exchange rate is:

Calculate the cost in AUD.

Exercise 5

A train ticket costs EUR. The exchange rate is:

Calculate the cost in AUD.

Exercise 6

Convert NZD to AUD using the exchange rate:

Complex Familiar Exercises

Exercise 7

Noah converts $ AUD into British pounds. The exchange rate is:

The currency exchange service charges a flat fee of $ before conversion.

Calculate the amount Noah receives in GBP.

Exercise 8

A traveller has USD remaining after a holiday. The exchange rate is:

The exchange service charges a fee of $ AUD after converting the money back to AUD.

Calculate how many Australian dollars the traveller receives after the fee.

Exercise 9

An online store lists headphones for USD. The exchange rate is:

Shipping costs $ AUD.

Calculate the total cost in Australian dollars.

Exercise 10

A hotel in New Zealand costs NZD per night. The exchange rate is:

A similar hotel in Australia costs $ per night.

Which hotel is cheaper? State the difference in Australian dollars.

Exercise 11

A tourist plans to spend JPY on food, JPY on transport and JPY on shopping.

The exchange rate is:

Calculate the total planned spending in Australian dollars.

Exercise 12

A bank advertises:

A travel card advertises:

Both charge no fees.

If Sofia converts $ AUD, how many more USD does she receive by using the better rate?

Homework Problems

Homework 1

Convert $ AUD to USD using:

Homework 2

Convert $ AUD to EUR using:

Homework 3

A backpack costs USD. The exchange rate is:

Calculate the cost in Australian dollars.

Homework 4

A tourist attraction costs JPY. The exchange rate is:

Calculate the cost in Australian dollars.

Homework 5

A traveller converts $ AUD into NZD. The exchange rate is:

The exchange service charges a $ fee before conversion.

Calculate the amount received in NZD.

Homework 6

A hotel costs EUR per night for nights. The exchange rate is:

Calculate the total hotel cost in Australian dollars.

Homework 7

An online order costs USD plus USD shipping.

The exchange rate is:

Calculate the total cost in Australian dollars.

Homework 8

A traveller compares two services for converting $ AUD to GBP.

Service	Exchange Rate	Fee
Service A		$
Service B		$ before conversion

Which service gives more GBP? Show calculations to justify your answer.

Next: GM Lesson 019 Shares, Dividends and Spreadsheet Models