Section B — Chapters 23–39
Applied Arithmetic II: Percentages in Action
Junior Cycle — 1st Year
- ✓Calculate a percentage of an amount to find tax paid and net income.
- ✓Calculate profit or loss and express it as a percentage of the cost price.
- ✓Calculate discounts and the resulting sale price.
- ✓Calculate compound interest for a small number of years by working year-by-year.
Key concepts
Income tax is a percentage of a person's earnings (gross income) that is paid to the government. The amount left after tax is paid is called net income.
The Cost Price (CP) is the price a shop pays for an item. The Selling Price (SP) is the price at which the shop sells the item to a customer.
If the Selling Price (SP) is greater than the Cost Price (CP), the shop makes a profit. If the Cost Price (CP) is greater than the Selling Price (SP), the shop makes a loss.
Profit or loss is often expressed as a percentage of the Cost Price (CP). This helps compare how well different items are selling.
A discount is a reduction in the original price of an item, often given during sales. The price after the discount is applied is called the sale price.
Interest is money earned on savings or paid on loans. With compound interest, the interest earned each year is added to the original amount (principal), and the next year's interest is calculated on this new, larger total. This means your money grows faster than with simple interest.
Key facts to remember
- 1Gross Income is your total earnings before any deductions.
- 2Net Income is your earnings after tax has been paid.
- 3Profit occurs when Selling Price > Cost Price; Loss occurs when Cost Price > Selling Price.
- 4Percentage profit or loss is always calculated on the Cost Price.
- 5A discount reduces the original price of an item.
- 6With compound interest, interest is calculated on the principal plus any accumulated interest from previous periods.
- 7To express a percentage as a decimal, divide by 100 (e.g., 25% = 0.25).
- 8Show all your working steps clearly in calculations.
Worked examples
Example 1
A shop buys a bicycle for €150 and sells it for €210. Calculate the profit and express it as a percentage of the cost price.
Answer
The profit is €60, which is a 40% profit.
Always calculate percentage profit or loss based on the Cost Price unless otherwise stated.
Example 2
A jacket originally costs €80. During a sale, it has a 25% discount. Calculate the discount amount and the sale price of the jacket.
Answer
The discount amount is €20, and the sale price of the jacket is €60.
Example 3
Aoife invests €500 in an account that pays 4% compound interest per annum. Calculate the total amount in her account after 2 years.
Answer
The total amount in Aoife's account after 2 years is €540.80.
Remember to add the interest to the principal each year before calculating the next year's interest.
Example 4
Liam earns a gross income of €450 per week. He pays income tax at a rate of 20%. Calculate the amount of tax Liam pays and his net income each week.
Answer
Liam pays €90 in tax, and his net income is €360 per week.
Common mistakes
- ✗Calculating percentage profit or loss on the Selling Price instead of the Cost Price.
- ✗Forgetting to add the interest to the principal each year when calculating compound interest year-by-year.
- ✗Confusing gross income with net income.
- ✗Incorrectly converting percentages to decimals or fractions (e.g., using 25 instead of 0.25 for 25%).
- ✗Making calculation errors, especially with decimals, when using a calculator.
Exam tips
- ★Read the question carefully to identify what is being asked (e.g., profit or loss, discount, final amount).
- ★Always show your full step-by-step working, even for simple calculations, as marks are often awarded for method.
- ★Double-check your calculations, especially when dealing with percentages and decimals.
- ★Make sure your final answer includes the correct units (e.g., €, %, years).
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