Calculate percentage increase and decrease, find the percentage change between two values, solve reverse percentage problems, and apply repeated percentage change including compound interest using multipliers.

What this dot point is asking

The Eduqas ratio content asks you to increase and decrease by a percentage, find the percentage change between two values, solve reverse percentage problems (find the original before a change), and apply repeated percentage change including compound interest. The multiplier method is the unifying tool, turning every percentage operation into a single multiplication. Percentages are among the most common real-life contexts on the paper (sales, pay rises, savings, depreciation), so this is high-value, with reverse percentages and compound interest being reliable Higher-tier tasks.

The multiplier method

The single most useful percentage technique is to convert a percentage change into a decimal multiplier.

So $250$ increased by $30\%$ is $250 \times 1.30 = 325$, and $250$ decreased by $30\%$ is $250 \times 0.70 = 175$. The multiplier method is faster than finding the percentage and adding or subtracting, and it generalises directly to repeated changes.

Percentage change between two values

To express a change as a percentage, divide the actual change by the original amount, then multiply by $100$. If a price rises from $40$ to $50$, the change is $10$, so the percentage increase is $\dfrac{10}{40} \times 100 = 25\%$. The crucial word is original: the change is always compared with the starting value, not the new one. Percentage profit and loss work the same way, comparing the profit or loss with the cost price.

Reverse percentages

A reverse percentage problem gives you the value after a change and asks for the original. The mistake to avoid is taking the percentage of the wrong number.

The key insight is that the discounted price represents $90\%$, not $100\%$, so you divide by $0.9$ rather than taking $10\%$ of $54$.

Compound interest and repeated change

Compound interest pays interest on the interest, so the same multiplier is applied once per period.

So 2000 pounds invested at $3\%$ per year for $4$ years grows to $2000 \times 1.03^4 = 2000 \times 1.12550\ldots = 2251.02$ pounds (to the nearest penny). Compound interest always beats simple interest over time because each year's interest itself earns interest, which is the comparison Eduqas often sets up explicitly.

Simple interest and other repeated changes

Simple interest, by contrast, pays the same fixed amount each year, calculated only on the original sum. For 2000 pounds at $3\%$ simple interest, the interest is $2000 \times 0.03 = 60$ pounds every year, so after $4$ years the interest is $4 \times 60 = 240$ pounds and the total is $2240$ pounds, less than the compound total of $2251.02$ pounds. The same compounding idea applies to any repeated proportional change, not just money: population growth, depreciation of a vehicle, and the decay of a radioactive sample all use $(\text{multiplier})^n$. When the rate changes between periods, multiply by each period's multiplier in turn rather than using a single power.

Why percentages matter

Percentages are the most common quantitative skill in everyday life and one of the most heavily tested on the paper, precisely because Eduqas wants candidates who can handle money and change confidently. Sales, tips, tax, interest, profit margins and population statistics are all percentage problems, and the multiplier method makes them all one technique. Mastering it, especially the reverse-percentage case that catches so many candidates, secures a reliable band of marks across both components.