---
title: "Compound Interest and Repeated Percentage Change"
description: "Applying a percentage change again and again multiplies rather than adds, so the multiplier raised to a power gives the answer in one step. The same calculation covers savings growing, a debt growing,"
canonical: https://lightmysky.com/learn/mathematics/compound-interest-and-repeated-percentage-change-mt_2vJz9VKle_
source: https://lightmysky.com/learn/mathematics/compound-interest-and-repeated-percentage-change-mt_2vJz9VKle_.md
retrieved: 2026-09-12
---

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# Compound Interest and Repeated Percentage Change

Applying a percentage change again and again multiplies rather than adds, so the multiplier raised to a power gives the answer in one step. The same calculation covers savings growing, a debt growing, and a value depreciating.

Subject: Mathematics · Area: Ratio & Proportion · Ages 14 to 15
Page: https://lightmysky.com/learn/mathematics/compound-interest-and-repeated-percentage-change-mt_2vJz9VKle_

## Ready when they can

- Turn a percentage rise or fall into a multiplier and use a power of it for n periods
- Show that a 10% rise followed by a 10% fall does not return to the starting value, and say why
- Compare the total repaid on a debt at simple and at compound interest over the same term

## Lesson: The multiplier does the repeating

Turn each percentage move into one multiplier. A rise of 5 percent becomes 1.05, and a fall of 20 percent becomes 0.8. Multiply the amount once and the whole step is done.

**Example.** Repeat a change by raising the multiplier to a power. A 500 pound deposit at 5 percent for 2 years is 500 times 1.05 squared, which is 551.25 pounds. The power counts the periods.

Equal rises and falls never cancel. A 200 pound jacket rises 10 percent to 220, then falls 10 percent to 198, because the cut applies to the new price. Simple interest pays on the original sum only, while compound pays on the growing total.

**Tip.** Debt shows the gap fast. Borrow 300 pounds for 2 years at 10 percent: compound asks 363 back while simple asks 360. Small rate gaps explode over many years, so starting early wins by miles.

**Recap.** Rise or fall becomes a multiplier, repeats become a power, and interest on interest is why the total outruns simple adding.

## Practice

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

## Needs first

- [Borrowing & Debt](https://lightmysky.com/learn/life-skills/borrowing-and-debt-mt_bAy4dmP1-A)
- [Percentages (age 12+)](https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x)