Calculate percentage increase and decrease, percentage change and reverse percentages, and solve financial problems involving simple interest, compound interest and repeated percentage change.

What this dot point is asking

WJEC places real financial mathematics at the heart of its number content, reflecting the strong everyday-money focus of the Welsh specification. You must calculate percentage increase and decrease, find a percentage change, work backwards through reverse percentages, and handle simple interest, compound interest and repeated percentage change. These appear mostly on the calculator Unit 2 and in worded, real-life contexts such as savings, sales, depreciation and bills, so a confident multiplier method is the key skill.

Percentage increase and decrease

The fastest method is a single decimal multiplier rather than finding the percentage and adding it on separately.

This multiplier method is faster, less error-prone, and extends straight to repeated change and compound interest.

Percentage change and reverse percentages

To express a change as a percentage, compare the change to the original amount, not the new one.

Percentage change $= \dfrac{\text{new} - \text{original}}{\text{original}} \times 100$. A profit of GBP 15 on a GBP 60 cost is $\tfrac{15}{60} \times 100 = 25\%$ profit.

Simple and compound interest

Interest is a percentage paid on a balance over time.

Simple interest adds the same fixed amount each year, calculated on the original sum only: $200$ at $5\%$ simple interest earns $200 \times 0.05 = 10$ each year, so GBP 30 over three years.

Compound interest pays interest on the new balance each year, so the growth compounds. Multiply by the same factor each period, which means raising the multiplier to a power.

So GBP 1000 at $4\%$ for $3$ years grows to $1000 \times 1.04^3 = 1124.86$. Repeated percentage change (population growth, depreciation) uses exactly the same power method.

Everyday financial contexts

The Welsh specification frames percentages in genuinely useful settings, so expect questions on pay, bills and value for money. A payslip question might ask for the income tax due once a tax-free allowance is removed, or the take-home pay after deductions. A "best buy" question gives two pack sizes and asks which is better value: divide price by quantity to get a unit cost (price per gram or per millilitre) and compare. VAT adds a fixed percentage to a net price, so a GBP 200 item plus $20\%$ VAT costs $200 \times 1.2 = 240$, and removing VAT from a gross price is a reverse percentage, dividing by $1.2$.

Depreciation and repeated change

Depreciation is compound decrease: a car worth GBP 12000 losing $15\%$ of its value each year is worth $12000 \times 0.85^n$ after $n$ years, so $12000 \times 0.85^3 = 7369.50$ after three years. The same structure models a population falling by a fixed percentage or a savings account growing. The single most marked decision in all of this is whether a change is a one-off (single multiplier), simple (add the same amount each period) or compound (raise the multiplier to a power), so read each question carefully for the word "each year".

Why this matters

Financial percentages are among the most heavily examined and most real-world parts of WJEC Mathematics, matching the specification's emphasis on personal finance and everyday numeracy. The multiplier method unifies increase, decrease, reverse percentages and compound change into one reliable approach, and recognising when growth is simple (add each time) versus compound (multiply each time) is the single most marked distinction in this topic.