Primary 6 Mathematics Learning Guide | Money Applications: Discount, GST and Interest

Wait, What? Money Problems Are Percentage Problems With a Reference Amount

Discount, GST and interest questions can feel like separate topics because the stories are different. Mathematically, they share one central challenge: identify the correct reference amount and apply the percentage to that amount. A 20% discount, a 9% GST charge and a 4% annual interest calculation are not solved by memorising three unrelated tricks. They are solved by controlling the base, the percentage and the sequence of changes.

This guide treats money applications as a branch of proportional reasoning. It focuses on the mathematical structure, not financial advice. Where real-world rates change over time, use the rate stated in the question or the current official context provided by the school or examination.

Every money percentage question has a hidden sentence: “100% represents which amount?”

Quick Answer

A reliable routine is:

NAME THE ORIGINAL AMOUNT → WRITE 100% → IDENTIFY THE CHANGE → FIND THE PERCENTAGE AMOUNT → ADD OR SUBTRACT → CHECK THE DIRECTION → CONFIRM THE FINAL BASE.

1. Discount Means a Reduction From an Original Price

If an item costs $200 and receives a 15% discount, the original price is the 100% base. The discount amount is 15% of $200, or $30. The sale price is $170.

The sale price can also be viewed as 85% of the original price.

Worked Example: Discount

A school bag costs $160 before a 25% discount. Find the sale price.

1. Original price = 100% = $160.
2. 25% is one quarter.
3. Discount = $160 ÷ 4 = $40.
4. Sale price = $160 − $40 = $120.
5. Check: a discount must reduce the price.

2. Find the Sale Price Directly When Helpful

A 30% discount leaves 70% of the original price. If the original price is $250, the sale price can be found directly as 70% of $250 = $175.

Both routes are valid: find the discount and subtract, or find the remaining percentage directly.

3. Reverse Discount: Find the Original Price

If a sale price of $84 represents 70% of the original price, the original price is not found by adding 30% of $84. The 30% discount was based on the original amount, not the sale price.

Use the unit method: 70% = $84, so 10% = $12 and 100% = $120.

4. GST Is an Increase Applied to a Taxable Amount

In school questions, use the GST rate stated or implied by the problem. Mathematically, GST is a percentage increase on the relevant pre-GST amount. If the rate in a question is r%, the total after GST is (100% + r%) of the taxable base.

The important issue is sequencing: if a discount applies before GST, the taxable base may be the discounted price rather than the original sticker price.

5. Discount Then GST Is Not the Same as Adding the Percentages

Suppose an item costs $100, receives a 20% discount and then a 10% tax is applied to the discounted price. The discount leaves $80. The tax is 10% of $80, or $8. Final price = $88.

It would be wrong to say “20% down and 10% up means 10% down overall” because the two percentages act on different bases.

6. Percentage Changes Multiply Across Stages

A 20% discount multiplies the original by 0.8. A later 10% increase multiplies the result by 1.1. Combined, the final amount is 0.8 × 1.1 = 0.88 of the original, or 88%.

This multiplicative view explains why equal-looking percentage changes do not simply cancel.

7. Interest as a Percentage of a Principal

For simple school problems involving annual interest, the principal is the original amount on which the stated interest percentage is calculated. If $1000 earns 4% simple annual interest for one year, the interest is $40.

For more than one year under a simple-interest interpretation, the same annual percentage is calculated from the original principal each year, unless the question states a different structure.

Worked Example: Simple Annual Interest

A sum of $1500 earns 3% simple annual interest for 2 years. Find the total simple interest.

1. Principal = $1500.
2. One year’s interest = 3% of $1500 = $45.
3. Two years’ simple interest = $45 × 2 = $90.
4. Total amount after adding the simple interest = $1590.

The exact interpretation should always follow the wording of the question.

8. Simple Interest and Compound Growth Are Different

Primary problems that explicitly state simple annual interest keep the principal base unchanged. Compound growth uses a changing base because earlier growth becomes part of the new amount. Do not import compound reasoning into a simple-interest question unless the problem asks for it.

This is another example of the changing-whole principle.

9. Money Units and Decimal Control

Money uses dollars and cents, so decimal place value matters. $7.50 is not the same as $7.05. When a percentage result produces fractions of a cent, follow the rounding instruction or school convention stated in the question.

Do not round earlier than necessary in a multi-step problem.

10. Find the Percentage Amount First When the Story Is Dense

For a complicated shopping problem, name each stage separately: original price, discount amount, discounted price, tax amount, final price. This prevents one amount from silently replacing another.

A before-and-after table is often useful.

11. Before-and-After Table

Stage	Reference amount	Change	New amount
Original	100%	None	Original price
After discount	Original price	Subtract discount	Discounted price
After GST/tax if applicable	Specified taxable base	Add percentage charge	Final amount

12. Multi-Item Discounts

If several identical items receive the same percentage discount, it may be easier to find the discounted unit price first and then multiply by the number of items. Alternatively, find the total original cost first and apply the discount once. Both routes should agree.

Method comparison is a useful checking strategy.

13. Percentage Saving Versus Amount Saved

A saving of $30 and a saving of 30% are different quantities. The first is an absolute amount. The second is relative to an original price.

If $30 is saved on a $120 item, the percentage saving is $30 ÷ $120 × 100% = 25%.

14. Comparing Offers Requires a Common Basis

An offer of “$20 off” and an offer of “15% off” cannot be compared without knowing the original price. Convert both offers to final prices or to percentage savings using the same base.

This is a rate-and-percentage comparison problem, not a slogan comparison.

15. Worked Example: Discount Then GST

An item costs $240. It receives a 25% discount. A 10% tax, as specified in this example, is then applied to the discounted price. Find the final amount.

1. 25% discount leaves 75%.
2. Discounted price = 75% of $240 = $180.
3. Tax = 10% of $180 = $18.
4. Final amount = $198.
5. Check: the final amount is below $240 because the discount effect is larger than the later tax increase in this example.

16. Reverse Percentage in Money Contexts

If a final sale price after a 20% discount is $96, then $96 represents 80% of the original. One percent is $1.20 and 100% is $120.

Do not add 20% of $96. That would use the wrong base.

17. Common Error Families

Error	What it looks like	Repair
Wrong 100% base	Applies a later percentage to the original when the base changed	Write “100% = ___” at every stage
Percentage cancellation	Assumes 20% down then 20% up returns to original	Track the changing base
Reverse-percentage error	Adds the discount percentage to the sale price	Treat the sale price as the remaining percentage
Early rounding	Rounds a money amount before a later percentage calculation	Keep exact values until the final required stage
Amount-vs-percentage confusion	Compares $20 off directly with 20% off	Convert to a common basis
Interest-base confusion	Uses a changing base in a stated simple-interest problem	Follow the stated principal structure

18. A First-Weak-Link Diagnostic

1. Reference: Can the learner identify what 100% represents?
2. Percentage fluency: Can common percentages be found efficiently?
3. Change direction: Does the learner know whether the amount should rise or fall?
4. Stage control: Can different percentage changes be applied in the correct order?
5. Reverse reasoning: Can the learner reconstruct an original amount?
6. Money precision: Are dollars, cents and rounding controlled?
7. Check: Can the learner estimate the likely final range?
8. Transfer: Can the same percentage reasoning work across discount, tax and interest contexts?

19. Examination Control

• Write what 100% represents.
• Separate original, intermediate and final amounts.
• Apply percentage changes in the order stated.
• Keep money values exact until the required rounding point.
• Check whether the price should rise or fall after each stage.
• Use benchmark percentages such as 10%, 25%, 50% and 75%.
• For reverse questions, identify what percentage the known amount represents.

20. What Parents Can Ask

• “What does 100% represent?”
• “Is this percentage based on the original price or the new price?”
• “Should the final amount be larger or smaller?”
• “What percentage remains after the discount?”
• “Can you find the original price from the sale price?”
• “Did you round before you were supposed to?”

21. What Tutors Should Protect

• Base discipline. Every percentage stays attached to a reference amount.
• Stage separation. Keep each money change visible.
• Reverse reasoning. Practise known-final-to-original problems.
• Benchmark fluency. Use mental percentage anchors.
• Method comparison. Compare “find change then add/subtract” with direct remaining-percentage routes.
• Prompt reduction. Let the learner identify the base and sequence independently.
• Transfer. Change money stories while preserving the percentage structure.

22. Evidence Boundary

This page teaches the mathematical structure of school money problems. Real-world GST, banking and investment rules can change and may involve conditions not represented in a Primary Mathematics question. For school work, follow the values and assumptions given in the problem and the current official syllabus or examination instructions.

Continue the Primary 6 Mathematics Series

• Primary 6 Mathematics Learning Hub
• Rate, Unit Rate and Quantity per Unit
• Fractions, Decimals, Percentages and Ratio as Equivalent Representations
• Mathematical Communication, Working and Justification

The Quiet Return

Money problems become much easier when the learner stops memorising separate discount, tax and interest procedures and begins tracking the same underlying percentage system across changing reference amounts.

The mature Primary 6 money habit is to ask: what amount is 100%, what percentage change happens next, and what new amount becomes the base after that change?