Financial mathematics: simple interest, discounts and GST
Using mathematical modelling to solve real money problems: simple interest on savings and loans, percentage discounts, and adding or removing GST
About three lessons of 45 to 60 minutes
Why does a bank pay YOU to keep your money there?
Leave $2,000 in a savings account paying 5% interest a year, and a year later the bank hands you an extra $100, for doing nothing except leaving it there. That extra money is interest, and the same idea runs in reverse when you borrow: a loan charges interest, so paying it back costs more than what you borrowed. One formula, simple interest, describes both directions.
Away from interest, almost every price you see already has percentages baked in: a 'sale' has a discount taken off, and in Australia most prices already include GST (Goods and Services Tax) added on. This unit builds the tools to calculate all three: what an investment or loan is really worth over time, what you actually pay after a discount, and how to add or strip out GST from a price.
- Money left in a savings accountsimple interest is a percentage of the original amount, paid for every year it stays
- A personal loan or 'buy now, pay later' planinterest is the cost of borrowing, calculated the same way as savings interest
- A '30% off' sale signthe discount is a percentage of the marked price, subtracted before you pay
- A receipt showing 'includes GST'10% GST is already built into the price; working out the pre-GST amount means undoing that addition
What students will be able to do
Students will use the simple interest formula to find the interest earned or owed on an amount of money, calculate the sale price after a percentage discount, and calculate a GST-inclusive price from a GST-exclusive one (and vice versa), reviewing whether each answer is reasonable for the situation.
- I can calculate simple interest using I = P x R x T / 100, where P is the principal, R is the rate per year, and T is the time in years.
- I can find the total amount in an account, or the total repaid on a loan, by adding the interest to the principal.
- I can find the sale price of an item after a percentage discount, by first finding the discount amount.
- I can explain why two discounts applied one after another do not simply add together.
- I can add 10% GST to a price, and work backward from a GST-inclusive price to find the original (GST-exclusive) price.
Standards this unit teaches
- AC9M8N05Australian Curriculum v9 (ACARA)Model financial problems
Use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model.
- 7.RP.A.3Common Core (US)Percent problems
Use proportional reasoning to solve multistep percent problems such as tax, tips, and discounts. This unit's discount and GST sections apply the same reasoning; simple interest extends it into a new formula.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
- Grade 7 unit rates, proportional relationships & percent teaching unitfinding a percent of an amount, the core skill every calculation in this unit builds on
- Grade 6 percentages teaching unitconverting a percentage to a decimal or fraction before multiplying
- Percentage in the glossarya refresher on what a percentage actually represents
Words to teach and display
- Principal
- the original amount of money invested or borrowed, before any interest is added
- Interest rate
- the percentage of the principal charged or paid per year, usually written as an annual (per-year) rate
- Simple interest
- interest calculated only on the original principal, the same dollar amount every year (unlike compound interest, met later)
- Discount
- an amount subtracted from a price, usually given as a percentage of the original price
- GST
- Goods and Services Tax, a 10% tax added to the price of most goods and services in Australia
- GST-inclusive / GST-exclusive
- a price that already has the 10% GST added in, versus the same price before GST is added
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Simple interest: I = PRT / 100
ConcreteSimple interest is calculated only on the original principal, using the formula I = P x R x T / 100, where P is the principal (dollars), R is the annual interest rate (as a plain number, e.g. 5 for 5%), and T is the time in years.
Someone invests $2,000 at 5% per year for 3 years. Interest: I = 2000 x 5 x 3 / 100 = 30000 / 100 = $300. The total amount in the account after 3 years is the principal plus the interest: $2,000 + $300 = $2,300. Notice the interest is the SAME $100 every single year (2000 x 5 x 1 / 100 = 100), because simple interest never earns interest on the interest already paid, only on the original $2,000.
A loan of $1,500 charges simple interest at 8% per year. Find the interest owed after 2 years, and the total amount to be repaid.
- Identify P = 1500, R = 8, T = 2.
- I = P x R x T / 100 = 1500 x 8 x 2 / 100 = 24000 / 100 = 240.
- Total repaid = principal + interest = 1500 + 240 = 1740.
Answer: Interest = $240. Total repaid = $1,740.
- In I = PRT/100, what does each of P, R and T stand for?
- Why is the interest the same dollar amount every year under SIMPLE interest?
2. Percentage discounts
PictorialA discount is a percentage of the ORIGINAL price, subtracted from it. Always find the discount amount first (original price x discount percent / 100), then subtract it from the original price to get the sale price.
A jacket is priced at $80 and is 25% off. Discount = 80 x 25 / 100 = $20. Sale price = 80 - 20 = $60. A common shortcut, multiplying directly by (100 - discount%)/100 (here, 75% of $80 = $60), gives the same answer, but finding the discount amount first makes it clear exactly how much was saved.
An item costs $120 and is discounted by 30%. Find the discount amount and the sale price.
- Discount = 120 x 30 / 100 = 3600 / 100 = 36.
- Sale price = original price - discount = 120 - 36 = 84.
Answer: Discount = $36. Sale price = $84.
- Why do you calculate the discount from the ORIGINAL price, not the sale price?
- Estimate: is a 30% discount on $120 closer to $30 or $40? Check your estimate against the exact answer.
3. Adding and removing GST
AbstractGST adds 10% to a price. Going forward (price excluding GST to price including GST) is a straightforward addition: GST amount = price x 10 / 100, then total = price + GST. Going backward is trickier: a GST-INCLUSIVE price is already 110% of the original, so you divide by 1.10, you do NOT simply subtract 10% of the inclusive price.
A price excluding GST is $300. GST = 300 x 10 / 100 = $30. Price including GST = 300 + 30 = $330. Now reverse it: given the GST-inclusive price of $330, the ORIGINAL (GST-exclusive) price is 330 / 1.10 = $300, and the GST component is 330 - 300 = $30, matching exactly. If you had instead taken 10% off $330 (330 - 33 = $297), you would get the wrong answer, because 10% of $330 is not the same as the GST that was added to $300.
A receipt shows a GST-inclusive total of $220. Find the GST-exclusive price and the GST component.
- A GST-inclusive price is 110% (1.10 times) the GST-exclusive price.
- GST-exclusive price = 220 / 1.10 = 200.
- GST component = 220 - 200 = 20.
Answer: GST-exclusive price = $200. GST component = $20.
- Why can't you find the GST-exclusive price by simply subtracting 10% from the GST-inclusive price?
- If a GST-inclusive price is $110, what is a quick way to check the GST-exclusive price is $100?
Common misconceptions and how to address them
MisconceptionIn I = PRT/100, R is entered as a decimal (e.g. 0.05 for 5%) and the result is still divided by 100.
Why it happens: Students learn 'percent means divide by 100' from other contexts and apply it twice: once by converting R to a decimal, and again in the formula's own /100.
How to address it: In this formula, R is the plain percent NUMBER (5, not 0.05); the formula's own /100 is what converts it to a percentage. Write R as the number straight off the problem (e.g. '5% per year' means R = 5), and let the formula do the rest.
MisconceptionSimple interest earns interest on top of interest, growing faster each year.
Why it happens: Students have heard of compound interest (met in later years) and assume all interest works that way.
How to address it: Simple interest is calculated on the ORIGINAL principal only, every year, so it adds the same fixed dollar amount each year. Show the amount for year 1, 2 and 3 side by side: it increases by an identical $100 (for the $2,000 at 5% example) each time.
MisconceptionTwo successive discounts, like 20% off then an extra 10% off, add up to a 30% discount.
Why it happens: Students combine the two percentages directly instead of recognising the second discount applies to an already-reduced price.
How to address it: Apply the discounts one at a time: on a $100 item, 20% off gives $80, then a further 10% off $80 (not off the original $100) removes $8, leaving $72, not the $70 a flat 30% discount would give. The second percentage is always of the NEW, smaller amount.
MisconceptionTo remove GST from a GST-inclusive price, subtract 10% of that inclusive price.
Why it happens: The forward direction (add 10%) and backward direction (remove 10%) look like they should be opposite, equal-sized steps.
How to address it: The GST-inclusive price is 110%, not 100%, of the original, so 10% of the INCLUSIVE price is more than the actual GST paid. Divide the inclusive price by 1.10 to get back to the original, then subtract to find the GST amount, rather than taking 10% off the inclusive figure directly.
MisconceptionThe 'total' after simple interest is just the interest amount, forgetting to add back the principal.
Why it happens: The formula I = PRT/100 calculates interest only, and it is easy to stop there and report it as if it were the account balance.
How to address it: Interest is the amount EARNED or OWED, not the new total. Always ask: does the question want the interest, or the total (principal + interest)? State which one explicitly before reporting a final answer.
Guided practice (with answers)
1. Find the simple interest on $3,000 invested at 4% per year for 2 years.
Answer: $240, because I = 3000 x 4 x 2 / 100 = 24000 / 100 = 240.
2. Find the total amount in an account after $5,000 earns simple interest at 3% per year for 4 years.
Answer: $5,600, because I = 5000 x 3 x 4 / 100 = 600, and total = 5000 + 600 = 5600.
3. An item costs $45 and is discounted by 20%. Find the sale price.
Answer: $36, because the discount is 45 x 20 / 100 = 9, and 45 - 9 = 36.
4. An item costs $90 before GST. Find the GST amount and the price including GST.
Answer: GST = $9 (90 x 10 / 100 = 9); price including GST = $99 (90 + 9 = 99).
5. A GST-inclusive price is $220. Find the GST-exclusive price and the GST amount.
Answer: GST-exclusive price = $200 (220 / 1.10 = 200); GST amount = $20 (220 - 200 = 20).
6. Why does taking 20% off, then a further 10% off, save less money than a single 30% discount?
Answer: Because the second discount (10%) is taken from the already-reduced price, a smaller amount, not from the original full price, so the total money saved is less than 30% of the original price.
Independent practice worksheets
Practise simple interest, discounts and GST with computed, never-wrong answer keys.
Differentiation
- Give a written checklist for each formula: circle P, R and T in the question before substituting into I = PRT/100.
- For discounts, always compute the discount AMOUNT first and label it, before subtracting, rather than jumping straight to a shortcut percentage.
- Use only whole-dollar, whole-percent examples (no decimals) until the three formulas are automatic.
- Keep a worked reference card visible: 'add GST: x 1.10 or +10%', 'remove GST: divide by 1.10, never just subtract 10%'.
- Compare simple interest with compound interest on the same principal and rate over several years, and discuss why a lender might prefer one over the other.
- Investigate combining a discount AND GST on the same item, and whether the order (discount then GST, or GST then discount) changes the final price (it does not, since both are multiplicative, but many students assume it must).
- Research a real savings account or personal loan's advertised rate and calculate the real dollar cost or return over 1, 2 and 5 years.
- Explore how doubling the interest RATE compares with doubling the TIME invested, in terms of the effect on simple interest.
Assessment: exit ticket
A three-question exit ticket sampling simple interest, discounts, and GST.
1. Find the simple interest on $4,000 at 6% per year for 5 years, and the total amount after 5 years.
Answer: Interest = $1,200 (4000 x 6 x 5 / 100 = 1200); total = $5,200 (4000 + 1200).
2. An item costs $150 and is discounted by 40%. Find the sale price.
Answer: $90, because the discount is 150 x 40 / 100 = 60, and 150 - 60 = 90.
3. A GST-inclusive price is $220. A student says the GST-exclusive price is $198 (by subtracting 10% of $220). Explain the error and give the correct GST-exclusive price.
Answer: The error is subtracting 10% of the INCLUSIVE price; the inclusive price is 110% of the original, so you must divide by 1.10, not subtract 10%. The correct GST-exclusive price is $200 (220 / 1.10 = 200).
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 simple interest (section 1), Lesson 2 discounts (section 2), Lesson 3 GST plus the exit ticket (section 3 and assessment).
- This unit assumes comfort finding a percentage of an amount (the Grade 7 ratios/percent unit). Revisit that first if 'x percent / 100' still needs scaffolding.
- Language to keep repeating: principal is the STARTING amount; interest, discount and GST are all a percentage of some base amount, and the base amount is different in each case (principal for interest, original price for a discount, GST-exclusive price for GST), which is exactly why the reverse-GST calculation needs division, not simple subtraction.
- The bar-model figure in section 1 deliberately shows the total splitting into principal and interest as a part-whole relationship, the same visual grammar this site uses for every other part-whole bar model, so simple interest is not introduced as an unfamiliar new picture.
- Curriculum note: AC9M8N05 (Australian Curriculum v9) is the sole Year 8 Number descriptor covering financial mathematical modelling; this unit's discount and GST sections also reinforce 7.RP.A.3 (Common Core) multistep percent problems, one year level down.
- Present mode and print both work: use the Print button for a clean handout, or project the page and work the reverse-GST worked example live, since it is the misconception most classes get wrong first.