Percentages and Simple Interest

This lesson covers DfE content statements L1.13, L1.14, L1.18 and L1.19 — understanding percentages; finding percentages of amounts in multiples of 5%; calculating percentage increases and decreases; and working out simple interest.

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What Is a Percentage?

"Per cent" means "out of 100". So 25% means 25 out of every 100.

pie title 25% shaded
    "25%" : 25
    "Remaining" : 75

Everyday examples:

• A 10% discount means you save £10 for every £100 spent.
• 50% means half.
• 100% means all of it.

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Key Percentage Equivalences

You should know these by heart (you met them in the fractions lesson too):

Percentage	Fraction	Decimal
5%	1/20	0.05
10%	1/10	0.1
15%	3/20	0.15
20%	1/5	0.2
25%	1/4	0.25
30%	3/10	0.3
40%	2/5	0.4
50%	1/2	0.5
75%	3/4	0.75
100%	1	1.0

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Finding Percentages of Amounts

At Level 1 you need to find percentages that are multiples of 5% (5%, 10%, 15%, 20%, 25%, etc.).

The Building Blocks Method

The idea is simple: find 10% and 5% first, then build up any percentage you need.

To find	Do this
10%	Divide by 10
5%	Find 10%, then halve it
1%	Divide by 100 (useful as a check)
20%	Find 10%, then double it
25%	Divide by 4
50%	Divide by 2

Worked Example — Finding 10%

Scenario: A coat costs £85. There is a 10% discount. How much is the discount?

10% of £85 = £85 ÷ 10 = £8.50

Worked Example — Finding 15%

Scenario: A restaurant bill is £60. You want to leave a 15% tip. How much is the tip?

10% of £60 = £6 5% of £60 = £3 (half of 10%) 15% = 10% + 5% = £6 + £3 = £9

Worked Example — Finding 35%

Scenario: A gym membership is £240 per year. Members get 35% off if they pay upfront. How much do they save?

10% of £240 = £24 30% = £24 × 3 = £72 5% of £240 = £12 (half of 10%) 35% = 30% + 5% = £72 + £12 = £84

Worked Example — Finding 25%

Scenario: A sofa costs £480. It is reduced by 25%. How much is the discount?

25% = 1/4 £480 ÷ 4 = £120

Exam Tip: In the non-calculator section, always start by finding 10% (divide by 10). From 10% you can build up any multiple of 5%. Show each step clearly — examiners give marks for method.

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Percentage Increase and Decrease

Percentage Increase

New amount = Original + Percentage of original

Worked Example — Price Increase

Scenario: A train ticket costs £45. The price goes up by 10%. What is the new price?

10% of £45 = £4.50 New price = £45 + £4.50 = £49.50

Percentage Decrease (Discounts)

New amount = Original − Percentage of original

Worked Example — Sale Discount

Scenario: A laptop costs £360. It is on sale with 20% off. What is the sale price?

10% of £360 = £36 20% of £360 = £36 × 2 = £72 Sale price = £360 − £72 = £288

Worked Example — VAT (Value Added Tax)

Scenario: A builder quotes £800 plus VAT at 20%. What is the total including VAT?

20% of £800 = £160 Total = £800 + £160 = £960

Worked Example — Successive Calculations

Scenario: Electricity costs £120 per month. The price rises by 5%. Then the new price rises by another 10%. What is the final monthly cost?

Step 1 — 5% increase: 5% of £120 = £6 New price = £120 + £6 = £126

Step 2 — 10% increase on the NEW price (£126): 10% of £126 = £12.60 Final price = £126 + £12.60 = £138.60

Exam Tip: When there are two percentage changes, always apply the second change to the NEW amount, not the original. This is a common mistake that costs marks.

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Simple Interest

Simple interest is charged (or earned) on the original amount only. At Level 1 you deal with interest rates that are multiples of 5%.

The Formula (in Words)

Interest = Original amount × Rate (as a decimal) × Number of years

Or, more simply:

1. Find the percentage of the original amount (that is one year's interest).
2. Multiply by the number of years.

Worked Example — Saving