Money Calculations
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
Worked example
Working out the change
(a) Ola buys 4 sandwiches at £3.85 each and 3 drinks at 70p each. Work out her change from a £20 note.
(b) Bus tickets cost £2.90 each. Work out the greatest number of tickets Ola can buy with £20, and her change.
Solution:
- (a) Put both prices in pounds first: 70p = £0.70
- Sandwiches: 4 × 3.85 = 4 × 4 − 4 × 0.15 = 16 − 0.60 = £15.40
- Drinks: 3 × 0.70 = £2.10
- Total cost: 15.40 + 2.10 = £17.50
- Change: 20 − 17.50 = £2.50
- (b) 20 ÷ 2.90 = 6.89…, and part of a ticket cannot be bought, so round down to 6 tickets
- Check: 7 tickets would cost 7 × 2.90 = £20.30, which is more than £20
- Change: 20 − 6 × 2.90 = 20 − 17.40 = £2.60
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
Check a conversion by its size
Currency conversion was set in 9 of the 22 papers, always on Paper 3. A one-step conversion is one mark for the answer alone, so a conversion done the wrong way round scores nothing. Check the size before you write it down: with 1 euro = £0.84, a pound is worth more than a euro, so £300 must buy more than 300 euros (300 ÷ 0.84 = 357.14 euros).
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