MathematicsExam code: 0580
Time, Currency and Conversions
Number
Calculating with money
- Amounts are normally written to two decimal places, and the second decimal is kept even when it is zero
- A calculator showing 1.4 is written as £1.40
- For large amounts the context may justify rounding to the nearest whole unit instead
- Money questions frequently combine with percentages, so read carefully for a discount, an increase or a rate of interest
Converting between currencies
- An exchange rate states what one unit of a currency is worth in another
- Converting in the direction the rate is written means multiplying, and converting back means dividing
- With £1 = $1.24, a sterling amount is multiplied by 1.24, and a dollar amount is divided by 1.24
- Where two currencies have no direct rate, convert through the one they share, in two separate steps
Exam tip
Write each converted amount on its own line
When a currency question takes more than one step, through a third currency or to compare two prices, write each converted amount down before going on, like the 40 875 yen below. That amount, or the conversion that gives it, earned a mark of its own in every such scheme, so a slip in the last step still keeps a mark.
Worked example
Converting through a third currency
The exchange rates are 1 euro = 163.5 yen and 1 pound = 187.9 yen. Convert 250 euros into pounds.
Solution:
- Convert euros to yen first, multiplying because the rate is written from euros
- 250 × 163.5 = 40 875 yen
- Convert yen to pounds, dividing because the rate is written from pounds
- 40 875 ÷ 187.9 = 217.535…
- Rounded to two decimal places, the amount is £217.54
Worked example
Comparing prices in two currencies
A phone costs 720 euros in France and £615 in the UK. The exchange rate is £1 = 1.18 euros. Find the difference between the two prices, in pounds.
Solution:
- The difference is wanted in pounds, so change the euro price into pounds first
- The rate is written from pounds, so euros to pounds is a division: 720 ÷ 1.18 = 610.169…
- Subtract: 615 − 610.169… = 4.830…
- The UK price is higher by £4.83
- Subtracting in euros instead (615 × 1.18 = 725.70, and 725.70 − 720 = 5.70 euros) gives the difference in euros, so it must still be changed into pounds: 5.70 ÷ 1.18 = £4.83