Exchange Rates (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note
Exam code: 3320
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Exchange rates
Exchange rates are used to compare and convert between different currencies.
How do I convert between currencies?
Start by writing the exchange rate
£1.00 (GBP) = €1.17 (EUR)
To convert from GBP to EUR, multiply by 1.17
Because 1.00 × 1.17 = 1.17
To convert from EUR to GBP, divide by 1.17
Because 1.17 ÷ 1.17 = 1.00
To find £28 in Euros
28 × 1.17 = €32.76
To find €75 in Pounds
75 ÷ 1.17 = £64.10 (to the nearest penny)
Examiner Tips and Tricks
If you can't work out whether to multiply or divide when converting currency:
Work out the value if multiplied, and write it down
Work out the value if divided, and write it down
Look at the exchange rate and consider if you are expecting a bigger number than the original, or a smaller number
Select the correct answer!
Worked Example
On a particular day, the exchange rate from US Dollars to Japanese Yen is:
1 US Dollar = 155.62 Japanese Yen
and the exchange rate from Australian Dollars to Japanese Yen is:
1 Australian Dollar = 102.09 Japanese Yen
An item costs 40 US Dollars.
Find the cost of the item in Australian Dollars.
Answer:
The first exchange rate is 1 US Dollar = 155.62 Japanese Yen
So to convert from US Dollars to Japanese Yen, multiply by 155.62
40 × 155.62 = 6224.80 Japanese Yen
The second exchange rate is 1 Australian Dollar = 102.09 Japanese Yen
So to convert from Japanese Yen to Australian Dollars, divide by 102.09
6224.80 ÷ 102.09 = 60.9736... Australian Dollars
Round to 2 decimal places as we are dealing with money
60.97 Australian Dollars
What is commission?
If you use a company to exchange currencies for you, they will add an extra charge, known as commission, for providing this service
Commission is usually a percentage of the value being exchanged
Examiner Tips and Tricks
Companies that exchange currencies and charge a commission are called foreign exchanges.
The foreign exchange will exchange the money you give them, but then take off the commission
E.g. If you swap £100 to Euros using £1.00 (GBP) = €1.17 (EUR) with a 2% commission charged
£100 × 1.17 = €117 is what you "should" receive
Then subtract 2% of €117 for commission (which is equivalent to finding 98%)
117 × 0.98 = €114.66 is what you actually receive
The foreign exchange has made (117 - 114.66) = €2.34 in commission
You could write this as £2, they have the same value at the given exchange rate
Different foreign exchanges will charge different rates of commission
They may also offer slightly different exchange rates between the currencies
Both of these methods are how foreign exchanges make a profit
Both factors should be considered when deciding where to exchange money
Worked Example
A foreign exchange charges 1.5% commission when purchasing Australian Dollars ($).
Their exchange rate to pounds is $1.00 = £0.52.
(a) Taking into account the commission, calculate how many Australian dollars you would receive if you exchanged £500.
Answer:
Change £500 into Australian Dollars
500 ÷ 0.52 = $961.54384615...
Decrease this by the commission (1.5%)
This is equivalent to finding 98.5% (a multiplier of 0.985)
$961.54384615... × 0.985 = $947.1153846
Round to the nearest cent
$947.12 received
(b) How much commission has the foreign exchange earned? Express your answer in pounds.
Answer:
You could subtract the answers above and convert back to pounds
But it is quicker to find 1.5% of £500 (as they want the answer in pounds)
0.015 × £500 = £7.50
£7.50 in commission
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