---
title: "Percentages (age 12+)"
description: "Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest"
canonical: https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x
source: https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x.md
retrieved: 2026-10-19
---

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# Percentages (age 12+)

Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest

Subject: Mathematics · Area: Ratio & Proportion · Ages 12 to 14
Page: https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x

## Ready when they can

- Calculate a 15% increase on £240 using a decimal multiplier (× 1.15)
- Find the original price before a 20% discount resulted in a sale price of £64
- Calculate simple interest on £500 at 3% per annum for 4 years

## Lesson: Percentage increase, decrease and simple interest

You already know how to find a percentage of an amount. Now you'll use that skill to increase or decrease an amount by a percentage, work backwards to find an original amount, and calculate simple interest on savings.

**Example.** A jacket costs £180. The shop raises the price by 15%. To find the new price in one step, multiply by 1.15 (that's 100% + 15%). £180 × 1.15 = £207.

A decrease works the same way, but you subtract from 100% instead of adding. A 20% decrease means the new amount is 80% of the original, so you multiply by 0.80. To reverse this and find the original amount, divide the new amount by that same decimal instead of multiplying.

**Example.** A jumper is on sale for £56 after a 20% discount. The sale price is 80% of the original price, so divide by 0.80 to find it: £56 ÷ 0.80 = £70.

Simple interest is money a bank pays you each year for keeping savings with them. It's always worked out on the original amount, not on any interest already added. Interest = original amount × rate × number of years. For £350 at 4% per year, one year's interest is £350 × 0.04 = £14, so after 3 years it's £14 × 3 = £42.

**Recap.** To change an amount by a percentage, multiply by a decimal; to find the original amount, divide by that same decimal, and simple interest is original amount × rate × years, added fresh every year.

## Practice

16 questions on this page, each with its working shown.

## Needs first

- [Percentages as fractions](https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ)
- [Proportional Reasoning Vocabulary](https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-)
- [Calculating percentages](https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ)

## Opens up

- [Compound Interest and Repeated Percentage Change](https://lightmysky.com/learn/mathematics/compound-interest-and-repeated-percentage-change-mt_2vJz9VKle_)
- [Price Elasticity of Demand](https://lightmysky.com/learn/civics-and-economics/price-elasticity-of-demand-mt_4ktSwG3D5q)
- [Frequency tables, bar charts and pie charts](https://lightmysky.com/learn/mathematics/frequency-tables-bar-charts-and-pie-charts-mt_eKJG-0eC6D)
- [Percentage Change with Multipliers](https://lightmysky.com/learn/mathematics/percentage-change-with-multipliers-mt_uqclfF4OBR)