Percentages, Rates & Financial Maths
Percentage of a Quantity
Circle the correct answer.
35% of 200
12.5% of 80
8% of 450
150% of 60
Match Problem to Answer
Draw a line to match each financial problem to its answer.
Percentage Increase & Decrease
Circle the correct percentage change.
Price increases from $50 to $65. % increase =
Price decreases from $80 to $60. % decrease =
Population was 2000, now 2400. % increase =
Simple Interest
Use I = PRT/100. Circle the correct interest amount.
P = $500, R = 4% p.a., T = 2 years
P = $1000, R = 5% p.a., T = 3 years
P = $200, R = 10% p.a., T = 1 year
Best Deal?
Sort these offers from best to worst value for the buyer.
Exchange Rates
Use the rate: A$1 = US$0.65.
Convert A$200 to USD
Convert US$65 to AUD
Financial Problem Solving
Show all working and include units in your answers.
You invest $3000 at 6% simple interest per year. How much interest will you earn in 5 years? What is the total value of your investment?
A laptop costs $1200. Option A: 25% off. Option B: $280 off. Which is the better deal and by how much?
Reverse Percentage
Find the original price before the change.
Sale price $60 after 25% off. Original price:
Price after 10% increase is $110. Original price:
Price after 20% off is $48. Original price:
Profit and Loss
Draw a line to match each scenario to its correct profit or loss amount.
Unit Rates and Best Buy
Calculate the unit rate to find the best buy.
2 kg of flour for $3.00, or 5 kg for $6.50. Better value:
6 cans for $9.00 or 4 cans for $6.40. Better value:
A car travels 450 km on 50 L. Rate:
Compound Interest Introduction
Compound interest adds interest on the interest already earned. Use A = P(1 + r)ⁿ where r is rate as a decimal.
$1000 at 10% p.a. compound for 1 year:
$1000 at 10% p.a. compound for 2 years (interest in yr 2 is on $1100):
Difference between simple and compound interest on $1000 at 10% for 2 years:
Financial Comparison
Show all working and explain your reasoning.
A pair of shoes originally cost $150. They are discounted by 30%. Then there is a further 10% off the sale price. Is this the same as 40% off the original price? Show working to justify your answer.
You borrow $500 at 8% simple interest for 3 years. Your friend borrows $500 at 8% compound interest for 3 years. Who pays more interest and by how much? (For compound: use A = 500 × 1.08³ ≈ $629.86)
Real-World Financial Maths
Apply percentage skills to everyday situations.
- 1Find three items on sale at a supermarket or online store. Calculate the original price using the discount percentage and sale price.
- 2Compare two mobile phone plans. Work out the total cost per year for each (including monthly fees and any per-minute or per-GB charges) and identify the best value.
- 3Look up the Reserve Bank of Australia's current interest rate. Discuss with a parent: how does a higher interest rate affect borrowing money for a car or house?
Percentage Increase and Decrease — Multiplier Method
For an increase of r%, multiply by (1 + r/100). For a decrease, multiply by (1 − r/100).
Increase of 15%: multiplier =
Decrease of 30%: multiplier =
Increase of 5%: multiplier =
Decrease of 2.5%: multiplier =
The Chained Discount Trap
Show all working and compare carefully.
A jacket costs $200. Shop A gives 20% off, then 10% off the reduced price. Shop B gives 30% off the original price. Which is cheaper? By how much?
A share price rises 50% then falls 50%. Is the final price the same as the original? Show with a $100 example.
Percentage Terminology
Sort each term into the correct column.
Profit and Loss Percentage
Use % profit = (profit/cost price) × 100.
Bought for $40, sold for $50. % profit =
Bought for $120, sold for $90. % loss =
Cost $60, sold for $75. % profit =
Cost $200, sold for $150. % loss =
Interest Investigations
Show all working. Use I = PRT/100 for simple interest.
You invest $3000 at 6% simple interest per year. How much interest will you earn in 5 years? What is the total value of your investment?
You need $1000 total after 4 years using simple interest at 5% p.a. What principal do you need to invest now? (Rearrange the formula.)
Best Value — Consumer Decisions
Sort each set of options from best to worst value for the buyer.
Unit Rates and Comparison Shopping
Calculate the unit rate to find the best buy.
2 kg of rice for $3.20 or 5 kg for $7.50. Better value:
4 pens for $6.80 or 10 pens for $15.90. Better value:
Car A: 450 km on 40 L. Car B: 600 km on 55 L. Better fuel economy:
GST Calculations
Australia adds 10% GST to most goods and services. Show all working.
A plumber charges $350 before GST. What is the total bill including GST?
A restaurant bill including GST is $176. What was the bill before GST? (Divide by 1.1.)
A new car costs $28,000 plus GST. Calculate the total price and the GST amount separately.
Exchange Rates
Use the given rate to convert between currencies.
Rate: A$1 = US$0.65. Convert A$300 to USD:
Rate: A$1 = US$0.65. Convert US$130 to AUD:
Rate: A$1 = €0.60. Convert A$500 to euros:
Rate: A$1 = €0.60. Convert €150 to AUD:
Currency Conversion Word Problems
Show all working. Round to 2 decimal places.
An Australian tourist in Japan has A$800 to spend. The exchange rate is A$1 = ¥90. How much yen do they receive? If they spend ¥35,000, how many yen do they have left? Convert that back to Australian dollars.
A pair of shoes costs US$95. The exchange rate is A$1 = US$0.65. What is the price in Australian dollars? If the same shoes cost A$160 in Australia, are they cheaper overseas?
Financial Planning Scenario
Use percentages and rates to plan and compare. Show all working.
You earn $850 per week. You pay 19% income tax on earnings above $400. Calculate your take-home pay. (Assume you pay 0% tax on the first $400.)
You want to save for a $2400 bicycle. You save 15% of your weekly take-home pay from the previous question. How many weeks to save enough? Round up to the nearest whole week.
Percentage Problem Solving — Extended
Show all working for each multi-step problem.
A car was purchased for $18 000 and depreciates 15% per year. What is its value after 1 year? After 2 years? By how much has it depreciated in total after 2 years?
Three investors each put $5000 into different accounts for 3 years: Investor A gets 6% simple interest p.a., Investor B gets 5.5% compound interest p.a. (use A = 5000 × 1.055³), Investor C buys shares that gain 20% in year 1, lose 10% in year 2, gain 8% in year 3. Compare their final amounts.
Percentage Increase and Decrease — Set A
Use the multiplier method. Show working.
Increase $340 by 25%.
Decrease $650 by 18%.
A salary of $54 000 increases by 7%. New salary?
A population of 12 500 decreases by 4%. New population?
Finding the Percentage Change
Use % change = (change ÷ original) × 100. Show all working.
Price rose from $80 to $96. What is the % increase?
Temperature fell from 25°C to 20°C. What is the % decrease?
Sales went from $120 000 to $85 000. What is the % decrease?
Which Type of Rate?
Identify the type of rate for each context.
A taxi charges $2.50 per km plus a $4 flag fall. The $2.50 is:
A phone plan charges 10 cents per text. This is:
10% commission on sales is:
Comparing Rates — Phone Plans
Calculate the total cost for each plan under different usage levels.
Plan A: $30/month flat. Plan B: $15/month + $0.25 per GB. For how many GB of data are the plans equal in cost? Below this, which is cheaper?
Taxation — Progressive Rates
Australia uses a progressive income tax system. Calculate tax owed.
Tax brackets: $0–$18 200: 0%. $18 201–$45 000: 19 cents per $1 over $18 200. Taxable income: $35 000. Calculate the tax owed.
Ratio Problems
Solve each ratio problem. Show all working.
Share $360 in the ratio 3:2:1 between Alice, Bob and Carol.
Concrete is mixed in the ratio 1:2:3 (cement:sand:gravel). How much sand is needed if 4 kg of cement is used?
A map scale is 1:50 000. Two towns are 8.5 cm apart on the map. What is the real distance in km?
Financial Maths — Mixed Review
Show all working.
A $600 jacket is on sale at 15% off. Calculate the sale price. If GST (10%) is then added back to the sale price, what is the final price?
Find the original price of a television whose sale price is $918, which includes 8% GST. (Hint: $918 = original × 1.08.)
An investor invests $4000 at 6% p.a. simple interest for 4 years. What is the total amount at the end? What percentage of the total is interest?
Consumer Maths Investigation
Research and calculate.
Look up the price of a mobile phone that interests you. Find a buy-now-pay-later plan for it (or create a scenario: $800 phone, pay $100 now + 6 monthly payments with 20% interest on the unpaid amount). Calculate the total cost and the extra amount paid due to interest.
Salary and Savings Planning
Use rates and percentages to plan a financial scenario.
A part-time job pays $18.50 per hour. Tax of 21% is withheld. How much is the take-home pay for a 15-hour week?
After tax, 20% of weekly income is saved. How many weeks to save $600 for a holiday?
Commission and Wages
Calculate take-home pay in each commission scenario.
A sales agent earns $400 base salary per week plus 5% commission on all sales. This week sales totalled $3200. Calculate total weekly income.
A real estate agent earns 2.5% commission on property sales. How much do they earn from selling a $680 000 house?
Budgeting with Percentages
Use percentage guidelines to plan a budget. Show working.
Weekly take-home pay: $620. Apply the 50/30/20 rule. How much goes to needs, wants, and savings?
After 6 months, how much would be saved?
Percentage of a Quantity — Calculator Skills
Use π ≈ 3.14 or a calculator. Choose the correct result.
8.5% of $1240:
3.75% of $8000:
112% of $450:
0.5% of $9600:
Error Analysis — Percentage Mistakes
Find and correct the errors.
Student: 'After 20% off, $60 becomes $50 because 20% of 60 is $12, not $10.' What is wrong? Correct the answer.
Student: 'To find the original price when the sale price is $80 after 20% off, I subtract 20% from $80 to get $64.' What is wrong? Find the correct original price.
Reflection
Write a brief reflection on what you have learned.
Describe two real-world situations where you would need to calculate a percentage change. Write the calculation for each.
What is the difference between simple and compound interest? Which earns more over time and why?