Money and Financial Maths

Priya changes £350 into euros at €1.16 per £1. On holiday she spends €290. When she gets home she changes the euros she has left back into pounds at €1.20 per £1. How much does she get back?

• A£96.67✓
• B£139.20
• C£60.00
• D£100.00

Answer: £350 × 1.16 = €406. After spending €290 she has €406 - €290 = €116. Changing back at €1.20 per £1 means dividing: €116 ÷ 1.20 = £96.67. Multiplying by 1.20 instead gives £139.20.

Leah has £500 in an account paying 2% simple interest a year and another £500 in an account paying 3.5% simple interest a year. How much interest does she earn altogether in one year?

• A£55.00
• B£27.50✓
• C£17.50
• D£2.75

Answer: First account: 2% of £500 = £10. Second account: 3.5% of £500 = £17.50. Total interest: £10 + £17.50 = £27.50. Applying 5.5% to the whole £1,000 would give £55, which double-counts.

£1,200 is saved in an account paying 4% simple interest a year. What is the balance at the end of 3 years?

• A£144.00
• B£1,344.00✓
• C£1,349.84
• D£1,248.00

Answer: Simple interest is the same each year: 4% of £1,200 = £48. Over 3 years: 3 × £48 = £144. Balance: £1,200 + £144 = £1,344.00. £1,349.84 is the compound-interest balance, and £144 is the interest on its own.

A traveller changes £400 into US dollars at $1.27 per £1. The bureau keeps 2% of the pounds as commission first. How many dollars does she receive?

• A$500.00
• B$508.00
• C$314.96
• D$497.84✓

Answer: Commission: 2% of £400 = £8, leaving £392 to change. £392 × 1.27 = $497.84. Changing the full £400 gives $508, and dividing by 1.27 instead of multiplying gives $314.96.

Assume a tax-free personal allowance of £12,570 and income tax of 20% on all income above it. Jo earns £28,570 a year. How much income tax does she pay a year?

• A£3,200✓
• B£2,514
• C£5,714
• D£16,000

Answer: Taxable income is £28,570 - £12,570 = £16,000. Tax at 20%: 0.2 × £16,000 = £3,200. Taking 20% of the whole salary gives £5,714, which ignores the tax-free allowance.

A garage bill is £180 for parts and £95 for labour. A 10% loyalty discount is taken off the parts only, then VAT at 20% is added to the whole bill. What is the total?

• A£308.40✓
• B£257.00
• C£330.00
• D£297.00

Answer: Discount on parts: 10% of £180 = £18, so parts cost £162. Bill before VAT: £162 + £95 = £257. Adding 20% VAT: £257 × 1.2 = £308.40. Discounting labour as well gives £297, and £257 is the bill before VAT.

A house is insured for £150,000. The annual premium is 0.4% of the value. What is the annual premium?

• A£150
• B£600✓
• C£60
• D£40

Answer: Premium = 0.4% of £150,000 = 0.004 × £150,000 = £600.

A budget has £500 allocated. If £350 is spent, what percentage remains?

• A30%✓
• B35%
• C50%
• D40%

Answer: Remaining = £500 - £350 = £150. Percentage = (150/500) × 100 = 30%.

Sam's monthly take-home pay is £1,850. Rent is 40% of this, bills are £285 and food is £320. What percentage of Sam's take-home pay is left after these three costs, to 1 decimal place?

• A27.3%✓
• B32.7%
• C72.7%
• D60.0%

Answer: Rent: 40% of £1,850 = £740. Total costs: £740 + £285 + £320 = £1,345. Left over: £1,850 - £1,345 = £505. As a percentage: 505 ÷ 1,850 × 100 = 27.3%. 72.7% is the share that is spent.

£4,000 is paid into a savings account that pays 3% compound interest a year. How much is in the account after 2 years?

• A£4,240.00
• B£4,120.00
• C£4,360.00
• D£4,243.60✓

Answer: The balance is multiplied by 1.03 for each year: £4,000 × 1.03 × 1.03 = £4,243.60.

£2,500 is invested at 4% compound interest a year. What is it worth after 3 years?

• A£2,800.00
• B£2,704.00
• C£3,000.00
• D£2,812.16✓

Answer: The balance is multiplied by 1.04 three times: £2,500 × 1.04 × 1.04 × 1.04 = £2,812.16.

£8,000 is saved for 2 years at 2.5% compound interest a year. How much interest is earned altogether?

• A£400.00
• B£405.00✓
• C£200.00
• D£8,405.00

Answer: The balance after 2 years is £8,000 × 1.025 × 1.025, and taking the original £8,000 off that balance leaves interest of £405.00.

£1,000 is invested for 2 years at 10% a year. How much more interest does compound interest earn than simple interest over those 2 years?

• A£10✓
• B£21
• C£100
• D£1

Answer: Simple interest gives 2 lots of 10% of £1,000, which is £200 of interest. Compound interest gives £1,000 × 1.1 × 1.1 = £1,210, which is £210 of interest, so the difference is £10.

A van bought for £18,000 loses 20% of its value each year. What is it worth after 2 years?

• A£14,400
• B£10,800
• C£11,520✓
• D£7,200

Answer: The van keeps 80% of its value each year: £18,000 × 0.8 × 0.8 = £11,520.

A commercial coffee machine costing £640 depreciates by 25% a year. What will it be worth in 3 years' time?

• A£480
• B£270✓
• C£360
• D£160

Answer: The machine keeps 75% of its value each year: £640 × 0.75 × 0.75 × 0.75 = £270.

A car is worth £9,000 today, after losing 10% of its value over the past year. What was it worth a year ago?

• A£9,900
• B£8,100
• C£10,000✓
• D£10,800

Answer: £9,000 is 90% of last year's value, so last year's value is £9,000 ÷ 0.9 = £10,000.

A loan of £3,000 is charged simple interest at 6% a year for 4 years. How much interest is owed altogether?

• A£180
• B£787.43
• C£3,720
• D£720✓

Answer: Simple interest is charged on the original amount only, so it is 4 lots of 6%, which is 24% of £3,000 = £720.

A saver is comparing simple and compound interest on the same deposit at the same rate. Which statement is correct?

• ACompound interest pays interest on the interest already earned, so it grows faster✓
• BSimple interest is worked out each year on the balance including the interest added
• CThe two methods give exactly the same balance after the first two years have passed
• DCompound interest has to be worked out monthly, while simple interest is yearly

Answer: With compound interest each year's interest is added to the balance and then earns interest itself, so a compound account grows faster than a simple interest account paying the same rate.

A 200 g jar of coffee costs £4.50 and a 750 g jar costs £15.75. Which jar is better value, and what is its cost per 100 g?

• AThe 750 g jar, at £2.10 per 100 g✓
• BThe 750 g jar, at £2.25 per 100 g
• CThe 200 g jar, at £2.10 per 100 g
• DThe 200 g jar, at £2.25 per 100 g

Answer: 200 g jar: £4.50 ÷ 2 = £2.25 per 100 g. 750 g jar: £15.75 ÷ 7.5 = £2.10 per 100 g. The lower cost per 100 g is better value, so the 750 g jar wins at £2.10 per 100 g.

A 450 ml bottle of washing-up liquid costs £1.35 and is on a '3 for the price of 2' offer. A 1.2 litre bottle of another brand costs £3.00. Which gives the lowest cost per 100 ml?

• AThe 1.2 litre bottle, at 2.5p per 100 ml
• BA single 450 ml bottle, at 30p per 100 ml
• CThe 450 ml bottles on the offer, at 20p per 100 ml✓
• DThe 1.2 litre bottle, at 25p per 100 ml

Answer: On the offer, 3 bottles (1,350 ml) cost 2 × £1.35 = £2.70, which is 270p ÷ 13.5 = 20p per 100 ml. The 1.2 litre bottle is 300p ÷ 12 = 25p per 100 ml. One 450 ml bottle alone is 135p ÷ 4.5 = 30p per 100 ml. The offer is cheapest.

Phone deal A costs £22 a month for 24 months with nothing to pay upfront. Deal B costs £15 a month for 24 months plus £150 upfront. Which deal is cheaper over the 24 months, and by how much?

• ADeal B, by £18✓
• BDeal A, by £150
• CDeal A, by £18
• DDeal B, by £168

Answer: Deal A: 24 × £22 = £528. Deal B: 24 × £15 = £360, plus £150 upfront = £510. Deal B is cheaper by £528 - £510 = £18. Ignoring the upfront cost makes the gap look like £168.

Rice is sold in a 2 kg bag for £3.20, a 5 kg bag for £7.25 and a 10 kg sack for £15.50. Which is the best value?

• AThe 10 kg sack, at £1.45 per kg
• BThe 10 kg sack, at £1.55 per kg
• CThe 5 kg bag, at £1.45 per kg✓
• DThe 2 kg bag, at £1.60 per kg

Answer: Cost per kg: 2 kg bag £3.20 ÷ 2 = £1.60; 5 kg bag £7.25 ÷ 5 = £1.45; 10 kg sack £15.50 ÷ 10 = £1.55. The lowest cost per kg is £1.45, so the 5 kg bag is best value. The biggest pack is not always the cheapest per kilogram.

A café can buy milk in a 4-pint bottle (2.27 litres) for £1.65 or a 2-litre bottle for £1.50. Which is cheaper per litre?

• AThe 4-pint bottle, at about 41p per litre
• BThe 4-pint bottle, at about 73p per litre✓
• CThe 2-litre bottle, at about 66p per litre
• DThe 2-litre bottle, at about 75p per litre

Answer: 4-pint bottle: £1.65 ÷ 2.27 = £0.727, about 73p per litre. 2-litre bottle: £1.50 ÷ 2 = 75p per litre. The 4-pint bottle is slightly cheaper. 41p comes from dividing by 4 as if pints were litres.

Sausages come in a pack of 8 for £2.40, or a pack of 20 for £5.40 with a '10% off' sticker. Which pack is cheaper per sausage?

• AThe pack of 8, at 30p each
• BThe pack of 20, at 27p each
• CThe pack of 8, at about 24p each
• DThe pack of 20, at about 24p each✓

Answer: Pack of 8: £2.40 ÷ 8 = 30p each. Pack of 20: 10% off £5.40 is £0.54, so it costs £4.86, and £4.86 ÷ 20 = 24.3p each. The pack of 20 is cheaper. 27p each forgets the 10% discount.

A 2.5 litre tin of paint costs £18 and covers 30 m². A 5 litre tin costs £32 and covers 60 m². A wall needs 45 m² of coverage. What is the cheapest way to buy enough paint?

• ATwo 2.5 litre tins, costing £36
• BOne 5 litre tin, costing £32✓
• COne 2.5 litre tin, costing £18
• DOne tin of each size, costing £50

Answer: One 2.5 litre tin covers only 30 m², which is not enough. Two 2.5 litre tins cover 60 m² for £36. One 5 litre tin also covers 60 m² but costs £32. One of each covers 90 m² for £50. The cheapest option that covers 45 m² is one 5 litre tin.