Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Reverse Percentages & Compound Interest

In one sentence. Finding the original price before a change (the question everyone gets backwards), and money growing multiplier-on-multiplier.

Percentages — one of 3 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Jacob Bernoulli. Learn Reverse Percentages & Compound Interest, teach it, then defend it against Jacob Bernoulli.

Where this sits in the specification

Specification 4MA1, 1.6 Percentages — reverse percentage, compound interest. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 1.6 — Percentages — reverse percentage, compound interest

1 · Understand it

What it is

A reverse percentage question gives you the value AFTER a change and asks for the original: 'a coat costs £44 after 20% off'. Since 44 is 80% of the original, the original is 44 ÷ 0.8. Compound interest applies a growth multiplier repeatedly: £2000 at 2.5% for 3 years is 2000 × 1.025³.

Why it works

The change was applied to the ORIGINAL — a number you don't know — never to the final price. So you cannot 'add the 20% back on': 20% of £44 is a percentage of the wrong number. Division undoes the multiplier exactly: if original × 0.8 = 44, then original = 44 ÷ 0.8. Every reverse problem is that one line.

When a question is asking for it

Watch for AFTER-words: 'sale price', 'after the increase', 'now worth', 'including VAT'. They mean the given number is post-change — divide by the multiplier. Compound interest announces itself: 'per annum', 'each year', 'compound'.

How to hold it in your head

Draw the machine: ORIGINAL → [×0.8] → £44. To go backwards through a machine you invert it: £44 → [÷0.8] → original. Deciding whether to multiply or divide is just deciding which side of the machine your known number sits.

2 · The mistakes that cost marks

  • Adding the percentage back: £44 + 20% of £44 = £52.80 ≠ £55. The 20% was 20% of the ORIGINAL (£55), a bigger number.
  • Dividing by the percentage instead of the multiplier: 44 ÷ 0.2 = £220 is nonsense; the coat is 80% of original, so ÷0.8.
  • For an original before an INCREASE, dividing by 0.85 instead of 1.15 (or vice versa). Build the multiplier from the story first.
  • Compound interest as simple interest: interest earns interest, so use the power, not repeated adding of the same amount.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

A coat costs £44 in a 20%-off sale. Find its original price.

  1. Sale price is 80% of original: original × 0.8 = 44.
  2. original = 44 ÷ 0.8 = 55.
  3. Check forwards: 55 × 0.8 = 44 ✓

Answer: £55

£2000 is invested at 2.5% compound interest per annum. How much is it worth after 3 years?

  1. Yearly multiplier: 1.025.
  2. 2000 × 1.025³ = 2000 × 1.0768…
  3. = 2153.78 (to the nearest penny).

Answer: £2153.78

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — In a sale, everything is reduced by 20%. A coat's sale price is £44. Work out its original price. (answer in £)
  2. Grade 7 — After a 15% price increase, a rail ticket costs £80.50. What did it cost before the increase? (answer in £)
  3. Grade 8 — £2000 is invested at 2.5% per annum compound interest. Work out the value of the investment after 3 years, to the nearest penny. (answer in £)
  4. Grade 9 — A car's value fell by 18% in its first year and by 12% in its second. It is now worth £14 432. What was it worth when new? (answer in £)
  5. 9+ — £5000 grows to £5618 in 2 years at r% per annum compound interest. Work out the value of r. (answer in %)

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Reverse Percentages & Compound Interest, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Reverse Percentages & Compound Interest works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Reverse Percentages & Compound Interest against Jacob Bernoulli — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 10 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

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