Percentage Problems and Simple Interest

In short: To write an amount as a percentage, make a fraction of the whole and multiply by 100. A discount takes a percentage off and an increase adds one on. Simple interest is the same percentage of the starting amount every year: interest = amount × rate × years.

Before you start

• Changing between fractions, decimals and percentages, and finding a percentage of an amount (see Fractions, Decimals and Percentages).
• Simplifying fractions (see Types of Fractions and Equivalent Fractions).

One amount as a percentage of another

Discounts and increases

Percentages of percentages

40% of a class are girls, and 25% of the girls wear glasses. The girls who wear glasses are 25% of 40%, which is $\frac{1}{4}\times 40\%=10\%$ of the class.

Simple interest

When you save in a bank, the bank pays you interest. When you borrow, you pay interest. With simple interest, it is the same amount every year.

Quick summary

• Percentage of a whole $=\frac{\text{part}}{\text{whole}}\times 100\%$.
• All of something is 100%, so what is left is 100% minus the used part.
• A 25% discount means you pay 75%. A 15% increase means you pay 115%.
• Going up 10% then down 10% does not get you back where you started.
• Simple interest: $I=P\times R\times T$, the same amount each year.
• To find the starting price after a discount, work back from the percentage you paid.

Quiz