Australian Curriculum v9 / ACiQ Year 8 Mathematics - Unit 1 - Percentage change and simple finance

Percentage Change and Simple Finance | Year 8 Mathematics

Solve discounts, mark-ups, profit, loss and simple interest by keeping track of the correct starting amount.

Updated 2026-06-15 - 4 min read

Percentage change is about comparing a change to a starting amount. The hardest part is usually not the arithmetic. It is choosing the correct base.

In Year 8, percentage work becomes more realistic: discounts, mark-ups, profit, loss and simple interest. These contexts all use the same idea.

Increase and decrease

To increase an amount by a percentage, find the percentage of the starting amount and add it.

A \$60 jacket increases by 15 percent.

$15\%$ of $60$ is $0.15 \times 60 = 9$.

New price: $60 + 9 = 69$.

To decrease an amount by a percentage, find the percentage of the starting amount and subtract it.

A \$60 jacket is discounted by 15 percent.

Discount: $0.15 \times 60 = 9$.

Sale price: $60 - 9 = 51$.

Multiplier method

The multiplier method is faster and helps prevent mistakes.

  • Increase by 15 percent: multiply by $1.15$.
  • Decrease by 15 percent: multiply by $0.85$.

The original 100 percent is the whole amount. An increase adds to 100 percent. A decrease leaves less than 100 percent.

Reverse percentage questions

Some finance questions give the final amount and ask for the original. These need reverse thinking.

If a price after a 20 percent discount is \$64, then \$64 is 80 percent of the original price. The original price is:

$64 \div 0.80 = 80$

This is different from adding 20 percent to \$64. Adding 20 percent would use \$64 as the base, but the discount was based on the original price.

Reverse questions are common because they test whether you understand the base amount.

Profit and loss

Profit means the selling price is higher than the cost price. Loss means the selling price is lower than the cost price.

If a shop buys headphones for \$40 and sells them for \$52, the profit is \$12.

Percentage profit compares profit to the cost price:

$\frac{12}{40} \times 100 = 30\%$

The base is the cost price, not the selling price, because the question asks how much the original cost increased.

Simple interest

Simple interest is interest calculated on the original amount only. The formula is:

$I = Prt$

Here $I$ is interest, $P$ is principal, $r$ is the annual interest rate as a decimal, and $t$ is time in years.

If $P = 500$, $r = 0.04$ and $t = 3$, then:

$I = 500 \times 0.04 \times 3 = 60$

The total amount is $500 + 60 = 560$.

Showing reasoning clearly

Finance questions often have several steps. Write what each number means:

  • original price
  • discount or mark-up
  • new base after the change
  • final amount

This matters because a correct answer with unclear reasoning is hard to check.

Quick check

  1. Increase \$80 by 10 percent.
  2. Decrease \$80 by 10 percent.
  3. A \$30 item sells for \$42. What is the percentage profit?
  4. Find the simple interest on \$200 at 5 percent per year for 4 years.

Answers:

  1. $88$
  2. $72$
  3. Profit is \$12, so percentage profit is $\frac{12}{30} \times 100 = 40\%$.
  4. $I = 200 \times 0.05 \times 4 = 40$

Transfer task

Find a real sale, subscription, sports statistic or bank example. Write the original amount, the percentage change, the base used and the final amount. Then explain the most likely mistake someone could make.

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